Hiyas Lazs! You could do that because as long as the firearm is going directly to a manufacturer for repair, an individual may so ship.
Concerning the shipment of shotguns and rifles (NOT handguns) to other unlicensed individuals OUT OF STATE, you must use UPS or FedEx. If you find a licensee (FFL) in the State you are shipping to that will accept the shotgun and/or rifle, you can ship to that licensee by the U.S. Postal Service. No markings of any kind should be placed on the box indicating what the contents are.
You MAY ship shotguns and rifles INSTATE by the U.S. Postal Service. Same caveat regarding markings on box.
Handguns always require a common and/or contract carrier.
SO, the only way for you to legally ship a rifle (which fyi is defined as: "a weapon designed or redesigned, made or remade, and intended to be fired from the shoulder and designed or redesigned and made or remade to use the energy of an explosive to fire only a single projectile through a rifled bore for each single pull of the trigger") INTERSTATE, from a nonlicensee to a nonlicensee, is to use an FFL as an intermediary. It is important to note that you do NOT have to use an FFL on your end to ship the rifle, as long as the ultimate destination is an FFL in the foreign State. This FFL should would transfer the rifle to your son for a nominal fee, as discussed above, usually around $25.
Hope this helps.
Nim