Here's some info I found on a similar gun:
The M1922 has the checquered walnut grips, making it a 2nd variation and has a WaA140 stamp. From what I have read, the Wa140 is a 7.65 (32acp), but the magazine in stamped "9m/m"; which would be the .380 acp version
The serial number is out of the range of any list of serial numbers I have seen: 2164xx with no prefix or suffix. Need parts, firing pin snapped off.
Waffenamt inspector #140 worked at FN from late 1941 to the end of the German occupation. The Germans took over 9mm Browning (.380 ACP) pistols that were in the factory at the time of the occupation, but that caliber was not in their supply system so the guns made for them were all in 7.65 Browning (.32 ACP).
The serial number of that pistol would indicate manufacture in the mid to late 1930's; it would seem strange it was not taken over until late 1941, but in chaotic times, things get overlooked. The magazines of the two calibers seem to interchange as far as working goes, but there are slight differences and I would hesitate to call them interchangeable.
The firing pin is identical to that of the Browning Model 1910 and the Model 1908 Colt .25 ACP, which might help your search for the part. I think Gun Parts was having them reproduced. Breakage is common because they have a long tip that is also the ejector. They can be repaired by drilling out the front end and inserting a piece of drill rod, but that is costly and a last resort.
Some other info:
This is what the Blue Book of Gun Values has to say:
MODEL 1922 or 10/22FN - 7.65mm (.32 ACP) or .380 ACP cal., modified Model 1910 with 4 1/2 in. barrel, longer grip frame and mag., made for commercial sale as well as military and police contracts. Several hundred thousand made by Nazis during the occupation of Leige, Belgium 1940-44. Mfg. between 1922-83.
100% 98% 95% 90% 80% 70% 60%
$275 $250 $200 $175 $150 $125 $110
Add 150% if .380 ACP Waffenamt proofed.
Add 15% for A prefix serial number/
Add $100 minimum for special contract markings.
The model 10/22 and M1922 are the same pistol. The Model 1910 was modified by FN technicians for sale to Serbian armed forces in 1923. Also sold to France, Holland, Germany, Greece, Turkey, and other countries.