PBS was indeed in Italyicon. Obviously this puts 506 PIR out of the picture. Only two other Army Ground Forces units had 506th in its designation. One was an early war coastal artillery unit that was reorganized with a different number; the other was a AAA unit serving in the Pacific.

I know of no source for a complete listing of Army Air Forces or Army Service Forces units, but if you want to take a wild guess, there was a 3506th QM Car Co. in the 5th Army in Italy. This type of unit was authorized 24 Garands by T/O&E 10-57, February 23, 1944.