I found a couple of my photos of the very similar looking North Africa bring-back pistol that I mentioned in my post, above. Based on a response received from an Italian member on another forum, the pistol is a Spanish production copy of a Smith & Wesson revolver. These Spanish copies were imported to Italy c. 1916 for use by the Italian military.
BTW: The grips on the pistol I observed were replaced with ivory while my WWII vet friend was in India (although he still had in his possession one of the original grips - shown in the photos). My WWII vet friend acquired his pistol in India when he was in the USAAC stationed there (the pistol having been brought to India by a USAAC bomber pilot when the pilot was transferred to Italy from North Africa). As related to me by my WWII vet friend, the pilot's story was that he had obtained the pistol from an Italian "surrender pile" in North Africa; brought it with him to India; then gifted it to my friend.
So, I again suggest that you focus on a possible connection between Italy and/or North Africa and the bring-back vet's unit. Assuming, of course, that the unit listed on the war trophy retention authorization papers was the bring-back vet's unit during wartime. It is always possible that the bring-back vet had been transferred into another unit for purposes of rotation back to the US (and that the retention papers were created as part of the process of sending him home at war's end), in which case the unit listed on the Capture Papers will not accurately reflect his actual wartime service.