My dad moved from Kaliforniastan to Texas and still has a few rifles and shotguns (no handguns) behind the lines and would like to get them to his new home. What are his options, or is he stuck with having them shipped to an FFL in Texas for transfer?

Can he not go back and get the rest of his stuff (firearms) to complete his move?

-If he goes back, he can ship them himself to his address in Texas. He would be able to use USPS only as UPS/FedEx will not do nonlicensee to nonlicensee. He can only use USPS for rifles and shotguns.........no handguns, no frames, no receivers.
-He could fly back with them as checked baggage.
-If someone else ships them they would be required to ship to a licensed dealer. Your father would need to complete a 4473/NICS to regain possession.

The easiest way would be a road trip back to CA and just haul them back to Texas. Secure them in the vehicle and hit the road.