Supposing my father-in-law had a kidney transplant, and is on anti-rejection medication. He then travels to Italy and for some reason is incapacitated. Is it possible that I can ship, from the US, his supply of (lawfully prescribed) medication? Which company (UPS?) Will Italian Customs let it through?
It may be possible but it’s absurd.
If he happened to need medication which wasn’t available in Italy, his Italian doctors would be the ones who’d have to get it (or, more likely, something else). It would be much simpler and faster to let them do their jobs, specially given that they have the proper paperwork to get whatever medication is needed.
Customs would be about 1000000 times more likely to reject your shipment than something obtained through proper channels.
I know there is a well regarded transplant center in Palermo - they have a partnership with the University of Pittsburgh and my uncle helped set up their transplant pharmacology department.
Palermo being a regional capital of one of the poorer Italian regions, I have little doubt that in an emergency a major city hospital can help your FIL out.