If he is being assigned to Korea (or any other country for that matter) by the US military, there are two things he needs to do.
1) Make sure that his gaining unit will let him keep his firearms in the unit armory, and that bringing personal weapons does not violate any local regs or policies. Many unit armorers do not want to hassle with it and so many units have policies against it. The military also became very gun "unfriendly" under
Clinton's regime, and local regs may forbid some folks from bringing personally owned weapons.
2) Arrange shipment of the weapons through the military, either with his household goods or other personal property. They have all of the appropriate paper for this, and his current post should have an office that ships personal goods that does this that will be able to tell him exactly what he needs to do. He should not hand carry the weapons or take them with him unless he is going on a Military Airlift Command flight, and even then, it is a bad idea (and probably prohibited). Otherwise, he has to go through Korean Customs with them, and he will probably get the weapons confiscated and maybe even get arrested. It is legal for him to ship personal weapons through the same approved military channels that the rest of his property goes through, but trying to ship them otherwise could lead to his arrest.
He probably should not even bother. When I was in Korea 10 years ago, there was one, count 'em, one, place in the entire country that I knew about where you could go to if you wanted to shoot a privately owned weapon as a US serviceman. Given there are pretty strict regs about transport of weapons, and attempting to transport them between US posts for recreational shooting could very well place one in violation of Korean law (and Korean Jails are much worse than the ones here), he would be better off leaving them in the states. Not to mention the fact that he might get grief from Customs or ATF if he tried to bring back the high-capacity magazines he took over. There are just too many ways this could get screwed up.
Even if he is a REMF, when he gets to Korea, he will get a chance to shoot his M16 every month or two (unless things have really changed a lot). The Korean war never ended; they just had a cease-fire, so most units send there people to qualify every few months (as opposed to the usual once a year), and even the mechanics and clerks go to lots of live-fire training.