Is it the right type of booster?
First, you need more information about what the brand and model of booster seat they have. A four year old should be in a high-back booster, not a backless/seat-only booster. Also, in my experience, some boosters have a minimum requirement of 30 lb and some have a minimum requirement of 40 lb, which can make a big difference as far as whether a just turned four year old will be the right size and weight for that booster seat. So you definitely want to know what model they have so you can check whether it's appropriate for the size and weight of your child.
Identifying the Seat
In the likely possibility they have no idea what the model is, have them take a couple pictures for you, one of the seat as a whole, and one of any stickers on the bottom/back of the seat. You can look up the model from the manufacturer's website from the info on the stickers, or do a google image search on the brand name and color(s) of the fabric.
Obtain and Read Instruction Manual
Once you've identified the model, it should be fairly trivial to look up the suggested weights and sizes and other information about it's proper use from the instruction manual on the manufacturer's site. Often a height range is specified, but it is more an approximation than exact, since some children are tall in the torso, but other children are tall in the legs. The important part is the seat belt guide can be adjusted to the height of the child's shoulder. The specs on the carseat (check other websites if not on the manufacturer's site) should tell you the height from the base of the seat to the lowest and highest shoulder strap setting. If it doubt after doing your research, go to your favorite retail store and sit your child on a similar booster seat to double-check.
The instruction manual will have other useful information about safe use of the booster, such as making sure the seatbelt is going across their lap/hips, not their belly button, so read the whole manual to feel confident about how the booster should be used.
Skip the Buckle Extender
This is a fairly typical example of a buckle extender:
For short term use, such as a vacation, I would not bother with obtaining a seat-belt extender. The purpose of a seat belt extender would be to make it easier to reach the buckle from the booster seat, which might be useful if, say, you had a booster seat squished between two other carseats and the buckle was difficult to reach. These are very specific to particular car make and model (and sometimes which seat position). While the NHTSA does not have any specific information indicating they are unsafe, it does introduce one potential additional point of failure, so I would shy away from using one unless it solves a pressing problem.
