There are a couple of different possibilities here, and you're probably going to have to do a chamber cast to find out which one for sure; the "BUG" proofs are typically pre-war German, along with the "DRGM" ("Deutsches Reich Gebrauch Meister"/"Patented in Germany") marking, and the most likely possibility is the 22 Winchester Centre Fire. This was a popular small-game cartridge in Germany between the wars, and wildcatting that cartridge led to the 22 Hornet. A very similar cartridge, the 5.3x35R, was used in lots of drillings and vierlings as a small-calibre centrefire option, and if there's a pronounced shoulder in the chamber, it could even be the 5.6x33 Rook. A chamber cast should let you know which of these you're looking at.