There's only so many companies that had their hand in building 1851's at the time.
What's interesting is that there was a person named Luciano Amadi who imported the first 1851 into Italy, paid for the tooling, and then presented the initial order for 250 1851 revolvers to a gunsmith named Vittorio Gregorelli (BTW there were 2 Gregorelli gunsmiths, Vittorio and Beniamino*). Then could the FAGS initials stand for Gregorelli?
The article linked below states that Vittorio wasn't licensed to make guns (only parts), but the Italian gunsmith's database indicates that he was a gunsmith since 1958. So maybe that changed.
And he was also a parts supplier/manufacturer.
Coinicidentally, the same Luciano Amadi was also a founder of Armi San Paolo in 1971 along with some gentlemen from the recently defunct handgun manufacturer named Gradoga closed. The initals for Gradoga just so happen to be Fabrica Armi Gradoga [FAG] and the gentlemen who all joined together to form ASP with him were named Giacomo Grassi, Giuseppe Doninelli, along with a person named Gazzola.
So maybe Vittorio Gregorelli and/or Luciano Amadi was having his parts and/or some guns made by Gradoga because of their close contacts with these gentlemen, or to increase the production of 1851's. And the initials were different because these were subcontacted guns being built for Amadi's gun trading company.
Since Armadi already had the gun trading company, had previously invested in making 1851's with Gregorelli, would it make any sense that he would have 1851's produced anywhere else in 1969 using his own tooling or parts?
Or perhaps by then someone else all together was producing 1851's?