Steven,
The action was Mauser Oberndorf made. The Mauser markings could be left off at the request of the buyer, or taken off by the buyer( most likely left off). Suhl was the town, and had(has) a very good reputation for gunmaking. Having been made in Suhl, in a "Suhler Waffenfabrik"( Gun Factory from Suhl)was a sign of quality, in an advertising sense, rather than any kind of official sense. Whether he was the same one that made the shot guns is difficult to say, there were a lot of Schlegelmilchs in the business, some of which with the same/similar given name. You would have to confirm name/address/time frame fit both the shotguns and your rifle.
Mike