Concerning the BK and Jup 12, there was certainly a great mess at KMZ's in the 1950-52 years...

I own three of these Jup 12, from the years 1951 and 52. They are all different, either in diameter of the front aluminium barrel, or in the visible inside, near the beauty ring. Two of them have a thread for a 40,5mm filter,but not at the same place (!), two again have a (correct) Zeiss number....
The BK you show looks like one of my 1951 Jup 12, at least about the aluminium barrel, which is exactly the same. Idem for the inside with the design between the diaph range and the glass. My 5101884 belongs to a series of 2000 Biogons which were made only in LTM mount by Zeiss. So, if this BK has a Zeiss number around (2)84xxxx, it should be genuine...
But you will be sure only when the lens is in your hand...!
Amitiés. Jacques.