The performance benefit of using matched pairs (or triples or quads) of RAM sticks is pretty negligible, and sometimes not even supported on cheap laptops. There are a small number of memory-intensive tasks where the additional bandwidth is useful, but even there the difference is on the order of a 10% speedup. For the vast majority of desktop usage, you just need to be sure that you have “enough” RAM.
In other words, you’ll spend far more time researching this upgrade than he’ll ever save with an every-so-slightly faster computer. (Unless he uses it for something professional video editing or heavy-duty physics simulations.)
If it chokes for some reason you can try downloading and installing Speccy. Along with a host of other system information the Ram part shows memory slots used/free and memory type to help your search. That information also helps you pick a best upgrade since there might not be a free slot right now requiring replacing the smaller module.
It’s no longer important to buy “matched” modules from the same supplier (I’m not 100% sure it ever was). The earliest dual-channel PC’s used two 64bit channels as one synchronous 128 bit channel, worked at the speed of the slowest module, only worked up to the smallest size, or didn’t work at all. Also, there were many more varieties of memory modules available then than there are now.
But it’s still the case that computers use quad-channel or dual-channel memory, now interleaved to give better performance. For maximum memory speed, the computer wants to be able to read alternately from each of the channels. If you put in a 64Gbit memory module, and a 2Gb memory module, the computer is not going to be able to arrange all of that memory into 2,3 or 4 equal channels.
From your description, you have a 2-channel computer. It’s not clear that 2-channel interleave makes much difference to most people. Estimates are from 5% to 70% improvement in memory performance, which translates into from 0% to 70% improvement in user performance, heavily biased down towards the 0% end for most users.