Tl/Dr: The solution is best found in areas far away from the homework, like sports and martial arts. In those parts of life, your girlfriend's son may be able to find the opportunity to build the skills you want him to apply towards homework. Please forgive the length of the prose. Writing clearly is a skill I'm trying to develop, and I don't want to rush the content and lose the message.
The problem you describe is called a Hard Problem™. It's especially hard for "gifted" individuals. I, like many others who have answered this question, was considered a "gifted student," and I've spent many years fighting to solve this problem for myself. So, I guess in that sense, I should say "I hope it's a Hard Problem™, because I'm having to spend an awful lot of effort at it!"
I do believe the only valid answer is to help your girlfriend's son find his own purpose in the world. That's not to say that such a statement is easy to do, but hear me out. Hopefully I can explain myself well enough that a lightbulb will go off in your own head, so you can solve the problem your own way.
School has a lot of measurements in it; indeed much of modern life is measured. We get grades on homework, we get grades on exams, we do placement exams to get into college. We are told what time to arrive at work, how much our time is worth to our employer in dollars per hour. We measure a lot, and that can be a good thing. Measurement is a fundamental step in the refinement process we teach in Western civilization. You measure what you did, compare that to what you expected to do, and then adjust your behavior accordingly. It's called a "feedback loop," and it is essential for the way we control things everywhere.
Of course, not all measurements are meaningful; not all measurements add value. Consider the case which I'm certain we've all faced: We have scored a 98, 88, 92, and a 93 on previous exams, and we are about to take one last exam. We know that the grading system is only 5 letters and the best we can get, an "A," is given for any score 90 or higher. Thus, we caluclate "what is the lowest score I can get on this exam, and still get an A for the course." Anyone "gifted" can quickly determine they only need a 79 on the final test. Sure, they can get a higher score, but no outside entity is going to actually recognize the difference between a 79 and any higher score. And thus, if they have no internal reason to go any further, they slack off. Why waste precious energy trying for a 95 on the test?
I believe every student does this at least some time in their life, but for gifted students it is more of a problem. If you're doing so well that you can't meaningfully measure the difference between your actual results and your expected results, how can you improve? My parents found the obvious approach: aggregation. This is a well trod approach in science, where you take multiple samples and average them to get more fidelity in your response. They said "You are only allowed 2 B's on your report card."
And thus, as a brilliant little gifted student, I did the only thing I could do: I "allocated" those B's to the courses I expected to do worst in, and reset the game. once again, I could calculate the least effort required to achieve the goal. Strange how good us "gifted" people are at not doing too much work!
I empathize with my parents, as I do you. This creates a pattern in the "gifted" student that is terribly hard to fix. You see, the other solution that is typically used is to crank up the difficulty. This can't be done across the board. I was horrid at Art. Still am, though I do try to teach myself that I can do art every chance I get (no, you cannot see the results. Nobody can see the results of that venture... ever.) It has to be done selectively. And herein lies the problem. It is very hard for others to really understand what things are easy for a gifted student and what things hard hard. The line drawn between easy and hard is often not drawn in the same place for a "gifted" person as it is for others. Indeed, one of my personal theories on what makes someone "gifted" is that what they find easy is so different from normal people's "easy" that they seem brilliant.
Me, I was brilliant in Math. I regularly went well beyond my grade level in mathematics. Nothing was hard. I cackled maniacally when I learned Algebra and could solve all sorts of problems that had bugged me before. I smiled sweetly at Calculus's subtle integrals and derivatives. Linear Algebra was my B--.... no, I wont finish that sentence in polite company. Let's just say that I'm a programmer now, and linear algebra is the ground upon which I trod to solve problems. When my parents needed to push me, harder, to try to get more measurable data, they'd push me in math, because they knew I could take it.
Then came Differential Equations. Its just another math right? I should excel right? Think again. Something about how it was taught was utterly alien to me. Nothing makes sense about it. I hated it, and I became the poster child for exactly what you fear for your girlfriend's son. Rather than buckling down and studying hard, I reacted defensively. People seemed to think I should be having no trouble at all with this, so I was pushed to "do better" at Differential Equations.
I mentioned earlier that I think what makes "gifted" people gifted is that the line between easy and hard is different for them. Thus, things that are hard for most people are easy for them. Well, I do believe the opposite is true as well. Some things that are easy for other people can be terribly hard for a "gifted" person. People don't understand why it could ever be so difficult for us, because we're "so smart" and it's "so easy." So we learn from a very early age to compensate. I can't draw a face to save my life (My attempts at drawing faces are among the "artworks" I've done that will never see the light of day). But I can tell you, geometrically, why we have vanishing points in our paintings. Do you understand the subtle concepts of white balancing in photography that lead the dress to generate such confusion? Did you know that the subtle overlay of opposing colors like blue and yellow with comparable luminosity that gave movement to the impressionist paintings like van Gogh's The Starry Night? Oh you did know that? Excellent! Did you also know that the reason that effect works is that the brain processes brightness and contrast several stages before considering color (an evolutionary trait for survival in the Savannah), and it is the cognitive dissonance between two pigments with the same brightness and different color that yields that feeling of movement?
No? You didn't know that? Look, I know not only what you do, but why you do it. Clearly you have nothing to teach me. In fact I have something to teach you! Now you learn Art your way, and I'll learn it mine.
Easy, right? Of course it's easy. All I did was use what I find easy to bludgeon what you find hard into the ground and make myself feel superior. This argument should sound familiar, if you are close to a "gifted" student. I'm certain its quite frustrating. My apologies.
So, going back to the one Math course I ever had trouble with, the one that makes me a posterchild for your fears for your girlfriend's son, I hated Differential Equations. And so, I convinced myself, and everyone around me, that Differential Equations are useless. Nobody would ever use them. You know Bessel functions? They show up in differential equations on circular boundaries. Friedrich Bessel got his name on them for not solving them! C'mon, what kind of serious mathematical field is it where you can get your name on a function you didn't even solve! And so, I didn't really "learn" differential equations. I got the B I needed to continue on, and forgot everything I needed to learn... until the next semester. I was an Electrical Engineering student at the time. Did you know that every single {bleeping} thing you have to learn as an Electrical Engineering student in the last two years derives from Differential Equations? Well guess what I know now. Let's just say I graduated successfully. Technically, I even still made honors. I did good, right? Now I can go on to be a programmer, and never use those differential equations again!
Did you know many programmers spend a lot of time programming up numeric solutions to differential equations? Gosh I wish I knew that back then.
So back to your son. What can we do? If nobody around us can understand what we find difficult and what we find easy, we are obliged to learn to do it ourselves, alone. We develop methods of quickly measuring whether a task is easy, permitting procrastination, or hard, which means it's time to dodge the task because "nobody can do it." Those measurements start to take a foreground in our life. If I'm a procrastinator, doing things ahead of time is hard. Simply being smart enough to get away with doing it late is easy. I can measure that very easily by monitoring how I go about the tasks and confirming my own bias: I work better at the 11th hour.
Okay, so that was a lot of text. All of it focused on showing how important it is to be able to make meaningful measurements, and showing what goes wrong when you can't. It also focused on how gifted people may find different things easy or hard along lines you may not be able to predict. Thus, while it may seem easy for you to measure the value of not procrastinating, it may be exceedingly hard for him. Sure, you can teach him not to procrastinate, but the real lesson to be had is how to teach these things to himself. And for that, we need to take a detour, away from measurable things into the unmeasurable world.
The vast majority of our sensory input goes unmeasured, consciously. If you had to actually measure the sincerity of every smile you get as you walk down the street, your mind would go mad. Much of what life must be is fluid. You may be able to develop an algorithm to determine the sincerity of a smile, but it would require far too much computational power to use as you walk down the street.
Consider how we walk. Using the same "I know what you do better than you know yourself" style argument from above, did you know that a lot of your walking gait occurs before signals reach your brain? If you are walking, and bump your right hand on a table, your left leg will have already adjusted its gait before the signals have even reached the brain stem. If you had to measure how hard you hit the table, and react to it consciously, in a feedback loop, you'd fall. The feedback loop actually happens at a much lower level, below that which we can consciously measure.
There are activities we do which exercise this ability to operate without fully understanding what we are measuring. Sports require you to be moving with such ferocity that there is no time to measure. They may be a good place for your girlfriend's son to look for "the next thing." My personal favorite place to look is Martial Arts, where you must move with such control and precision that you literally cannot measure everything that matters. You must feel all of those little details that can't be measured on their own, and integrate them into a way to view the world that lets you grow.
Of course, you can do this yourself. Sports and Martial Arts are not magical things which turn procrastinators into upstanding individuals. They're merely places where you will find teachers who have already learned the subtle art of teaching these unmeasurable things. You can do it too, just with conversation alone. All you need to do is ensure that he has some influence over where the conversation is going, and you have some influence over where the conversation is going. If he ever seeks to dominate it, taking away your influence, you find some subtle point in the middle of his argument where you have influence, and make it important. If you ever find that you are dominating, look for a way to help him find things to push back with.
Sounds easy right? Sure.. I've been working on it for years, and expect to still be working on it when I die. There's a reason I like to defer to the Martial Arts teachers! They have entire schools of thought dedicated to how to teach this way of thinking about the unmeasruable unknowns. However, if you want to do it yourself, a general geometric argument I have found effective is to always nudge the conversation at right angles to the direction he is driving at, rather than directly opposing him. If you do that continually, you can drive the argument into a circle, but typically the other person will tire first, and permit you to start driving the argument for a while, and let him learn to push at right angles.
However, in the end, what you will teach him is far more valuable than how to not procrastinate. You'll teach him how to explore things in places he sees no immediate value in. You'll give him the set of skills to dive into such "valueless" spaces without wasting his time or energy (which he values greatly). Then, one day, he might decide to explore the idea of not-procrastinating, on his own. He doesn't see any benefit in doing things in advance, but he's learned techniques to explore such an idea without being wasteful. Lo and behold, he may discover that there is value in it that he never saw before!
And if it fails? Well, it could fail. I quite literally spent 30 years trying to learn the simple fact that it is worth learning how to do this. I'll keep learning how to do this until I die. However, all is not lost. Even if you cannot help him, all you really need to do is simply do no harm to him. He can serve as a sharpening stone for you to hone this skill yourself, and we are blessed to have such individuals in our lives. And, frankly, I've never met someone so stubborn that they can't learn from this approach, including myself! It can just take time, and so long as you feel you are becoming a better person through the process of trying to teach him, you can really take all the time you need.
