I'm hoping some folks here may shed some light on the background of this unique watch. I've posted it on MWR but so far no definitive consensus on its provenance has developed despite plenty of educational input. Also thanks to @DirtyDozen12 for his enlightening input. From my understanding the British Air Ministry ordered the Weems and the 6b/159 (ref 4830) during the war. Historically, "AM" signifying Air Ministry was utilized on the 6b/159 prior to 1943. This was later switched to a broad arrow with issue number containing an 'A' prefix after 1943 to signify The Ministry of Aircraft Production. This particular example dating from 1945 contains both the "AM" and broad arrow markings. Also this sei tacche watch has unusual fixed bars and is a larger 35mm in diameter. In addition, I cannot find any case reference 22919 in my research.
In my experience with Longines extracts, the numbers like 22919 are not reference numbers. They are often referred to as "order numbers" in the extract. Sometimes the reference number isn't obvious, but Longines will tell you if you request historical info. For example, my Longines WWW has the number 23088 on the caseback and the extract calls that the order number. The reference number is given as 5707, and is not anywhere on the case, which is typical.