This is also from the BATF website:
2. May I lawfully transfer a firearm to a friend who resides in a different State?
Under Federal law, an unlicensed individual is prohibited from transferring a firearm to an individual who does not reside in the State where the transferee resides. Generally, for a person to lawfully transfer a firearm to an unlicensed person who resides out of State, the firearm must be shipped to a Federal Firearms Licensee (FFL) within the recipient’s State of residence. He or she may then receive the firearm from the FFL upon completion of an ATF Form 4473 and a NICS background check. More information can be obtained on the ATF website at www.atf.gov
. The GCA provides an exception from this prohibition for temporary loans or rentals of firearms for lawful sporting purposes. Thus, for example, a friend visiting you may borrow a firearm from you to go hunting. Another exception is provided for transfers of firearms to nonresidents to carry out a lawful bequest or acquisition by intestate succession. This exception would authorize the transfer of a firearm to a nonresident who inherits a firearm under the will of a decedent. See 18 U.S.C. 922(a)(5).
Because we are talking a handgun and the buyer is under 21, this is why I suggested against doing the deal.