Quick review of Italian history and the Beretta 1934/35...... still a fine example of occupied German manufacture. .... is that a [ML] inspector stamp on the right trigger guard?
The Beretta factory was taken over by the German's after they rescued Mussolini from prison in 1943.
"The Gran Sasso raid refers to Operation Eiche ("Oak"), the rescue of Italian dictator Benito Mussolini by German paratroopers led by Major Otto-Harald Mors and Waffen-SS commandos in September 1943, during World War II. The airborne operation was personally ordered by Adolf Hitler, planned by Harald Mors, and approved by General Kurt Student. Gerhard Mertins was among the paratroopers who participated in the raid."
After that the factory no longer used the Italian Imperial IVU (4th technical control unit) marking on guns or the Fascist date since the Fascist era was over. Blank slided guns were made until the Germans decided what to do and since the IVU office was no longer valid and marked them with the Brescia proof. Later the office was designated 4UT ... basically the same marking but organized under German control.
Some later war BB prefix guns will have the 4UT marking after Brescia but the common thought is they were used from spare parts until they ran out of slides and made Mod. 1934 slides around serial number 7543BB like this gun dated 1944.
The last recorded Mo. 1934 slide is 7055BB in my DB so I have a big gap in that serial range for the slide transition.