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Mine is also double dated. I believe military weapons that were put back into service after WWI were stamped with a second 1920 date.
Based on a Weimar law from August 1920, the “1920” was an identification stamp for weapons in possession of the Reichswehr (army) and Sipo (security police).
Since this is often misunderstood, a brief explanation:
At the time, the government was trying to get military weapons out of civilian hands through a buyback. Some folks immediately blather about “gun control”, but this was mostly about heavy hardware; since the Imperial army never surrendered, but just dissolved more or less orderly, lots of people just took weapons home and then used them in the civil unrest of 1919/20. There are pictures of people standing in line clutching machine guns, flamethrowers, and mortar tubes, to collect the bounties.
To prevent guns from being “disappeared” and then turned in again, for more money, all were given the 1920 stamp when turned over to the Reichswehr.
Four military handguns are listed as falling under the regulation: the Reichsrevolvers M79 and M83, the Mauser C96, and the Luger in 9mm. Quite a few Mauser 1914’s have a 1920 stamp, even though they actually didn’t need one.
No civilian guns, longarms or handguns, were affected. But even among military guns, the success rate was moderate; many guns disappeared under floorboards or elsewise, and even heavy stuff like machine guns and even cannon were tucked away in clandestine armories of various political and paramilitary organizations.
So any double-date police Luger can safely be assumed to have come into police service most likely by way of a Reichswehr depot, which had lots of pistols on offer for any agency that asked.