In regards to the AA & BB suffix, these were used on the Model 1934 Beretta.
The following information comes from 3 books.
Pietro Beretta Le Automatiche:
In 1943, after the birth of the RSI, the fascist era was deleted from the slide leaving only the year of manufacture, page 324. Weapons of that time, even the ones produced for the Germans have the 4UT stamp, page 326. I could not find a reference in this book for the blank slides. I have a 1944 with slide legend & stamped 4UT.
German Pistols and Holsters, Vol II:
Page 138 Model 1935 serial number range, 500,000 - 507,000 Blank slide
507,000 - 600,000 Year stamp, no fascist stamp
600,000 - 616,000 Blank slide
Page 139 Model 1935, 4UT stamp applied initially near 515,000. From 515,000 - 536,000 both 4UT and Crown/Lion proof
Axis Arms:
Page 276 Model 1935 serial number range, 1943 date 495,000 - 500,000
" " " " " , 1943 " 500,000 - 508,000 RSI era
1944 " 508,000 - 600,000 RSI era
1945 " 600,000 - 620,799 RSI era
Many are 4UT marked, very few bear the Eagle/WaA162 stamp.
Maybe confusing, but I have 548,223 with slide legend dated 1944 & 4UT stamp. Your pistol may fit in there. If you need something else from the books, I'll try and dig it out.
Hope it helps
Don