1. The gun is not registered in Pennsylvania. There is no firearms registration in Pennsylvania.
2. Unless both persons were residents of the state of Arizona, it would violate Federal law to shake hands and say thank you for the gun, both the father and the son would be committing their own separate felonies if the father was a resident of PA and the son was a resident of Arizona.
3. Since the son is resident of South Carolina, and the father is a resident of Pennsylvania, Federal law (18 USC 922 (a)(3) and (a)(5)) requires that the father deliver the handgun to an FFL in South Carolina who will then transfer the handgun to the son. This has absolutely nothing to do with firearms registration as neither South Carolina, Pennsylvania, nor the Federal government registers firearms. It is 100% because the interstate transfer of firearms is regulated by the Federal government.
4. The father can hand carry the gun to a South Carolina FFL. The father can ship the gun to a South Carolina FFL via FEDEX or UPS. The father can take the handgun to a Pennsylvania FFL who can use US Postal Service to mail the handgun to a South Carolina FFL. All legal options.
5. The son fills out a form 4473 at the South Carolina FFL, gets a NICS background check done and receives the firearm. Filling out a form 4473 does NOT register the gun. Firearms registration in all but about 4 or 5 states in the US is a complete myth.