short answer, yes, BOTH transfers need to be completed thru a dealer.

Pa and NC both allow private party transfers of LONG GUNS ONLY.

Without researching the PA laws myself there MAY be an exemption of a gift or inheritance between family members BUT that is usually restricted to residents of that state only.

Ted beat me to the answer. He posted while I was still writing.

The fact that the pistol is "unregistered" may be meaningless, depending upon PA law and how long ago it was purchased. A PA dealer can tell you about that.

The very best way to go about this is for the son to come to PA in person, or the father to go to NC in person.
Second best would be for the father to leave the gun to the son in his will, because, in most states, bequests need involve neither feds nor state.

for the information.