Peter:
I can't recall but when did Italy join the International Proof Commission/Conference. I think it in 1920 or was just after WWI? It may have been on or just prior to December 30th, 1923 when proof became compulsory. The effective date was October 16th, 1924. I have seen dates as early as 1910 when Royal decrees were enacted for proof rules. I believe it was post 1928 that Beretta sporting weapons wear the touchmarks of the Gardone Val Trompia proofhouse. Considering economics and the uncertainty of War, I would look there 1st for a sourcing possibility. Now there are Beretta examples of wartime pistols that wear Belgian touchmarks. And as you note post WWI the Germans had a heavy hand in Belgium and by WWII there were strong connections to Italy. So a Beretta-Liege sourcing line did exist. It is interesting that the "12 c" in the rhombus closely resembles the Belgian & English chambre stamp. The Star holds significance with the Italian Republic and the change from the crown to the star is more than likely found there.
It is thought that Italy has some form of proof house as early as the 16th century. But you must remember that Italy did not exist as a nation.
Brescia was privately operated by 1910. In 1920 the government opened the Gardonne proof house and the Brescia proof house in 1921. Dec 30, 1923 the proof laws were signed. They took effect on Feb 8, 1925. The provisionally proofed shotguns were done at 14,700 psi.
There was some ability to proof an arm that had not been sold around 1920 until Sept 1, 1921. These guns were stamped "BPD".
The 12 C in a rhomus / diamond is not an Italian proof mark, but the Belgian gauge designation given to shotgun proofed using black powder. There was no Belgian export mark until 1924. The English bore designation would not have the C (for choke).
Beretta had been selling Scott and other English made shotguns up until the early 1930's, perhaps later.
Pete