Your gun is neither for the Luftwaffe nor early, as WaA 140 was primarity for the Wehrmacht. You have a gun that was made nearly at the end of the German occupation in the "c" suffix range.
German 1922s were first issued with serial numbers without letters from somewhere in the 20,000 range to 100,000. From 24127 (the lowest nazi gun # I have recorded over 40+ years) is WaA613.
At around 57-58,000 the WaA was changed to 103.
Somewhere around 63-64,000 the WaA was changed to 140.
Remember: Ca. 24,000-100,000 NO letter suffixes were used.
(Note: WaAs or "Waffen Amts" were numbers assigned to a particular inspector who had charge over the whole facility for inspection purposes to ensure that production ws suitable for the armed forces.)
#s rolled over into the 100,000 range, probably sometime in 1942, but had blocks interspersed that didn't use the "1" but, rather, used a shorter number, followed by the letter "a," connotating that the guns were in the 100,000 range. (Example: Between 102269 and 103693, I have recorded this #: 3626a (103626). Then, betwween 103693 and 107757 there is 5105a (105105), and 7633a (107633). The highest 6 digit #s I have recorded in the 100,000 range are 197396 and 197510, followed by 98024a (198024) and 99775a (199775).
Confused? It gets better.
In the "b" range, the lowest numbers I've recorded are 209b (200209) and 328b (200328). The first full 6 digit # I recorded is 204337. After that 5956b (205956), and so on. The highest full 6 digit # I have recorded is 217307. BTW, all 1922s from ca. 60,000 onwards are WaA 140, and are, by far the most common.
All the remaining #s in the the 200,000 range that I have recorded after my highest (217307) have all had "b" suffixes, and nobody has ever explained why #s with letter suffixes were used in blocks interspersed with full #s prior.
Somewhere in late '43, production began on the "c" range which was the 300,000 range. However, ALL guns in that range that I have recorded have "c" suffixes and NO full 6 digit #s. The highest "c" that I have recorded is 41797c (341797). It is generally accepted that FN made 363,200 guns (supposedly from German records), after which the Germans evacuated FN and Liege in Sept. 1944.
Your gun falls in the last range of production, made in 1944, and is the 320614th 1922 made under occupation if German records are to be believed. and, although black grips may have been used on it (factory leftovers), the most common type of grips encountered on high number gusn are the checkered wooden ones. Without seeing your grips, I really couldn't say for sure. They might be post-war replacements.
(Note: I have lost interest in my 1922 project, but if anyone is doing research on them, I will be happy to provide a complete list of all serial #s that I have collected over the last 40+ years. I have other 1922 lists as well as Nazi guns.)