Depends on whether or not he has a green card (i.e. a permanent resident alien), or he's here on some kind of work (or student) visa.

If the former, his federal gun rights are exactly the same as a U.S. citizen, and he can purchase firearms, get FFLs, etc.  If the latter, he needs a valid hunting license in order to purchase a firearm.

(Note that there can sometimes be additional state-level laws that affect non-citizens.  For example, in MO, a non-citizen cannot legally purchase a handgun, but long guns are fine.)