The post-war Stoeger catalogs refer to the West German product as the Model VIII, (with and "E" after that if it had an ejector). So does the history referred to.

The Sauer assets in Suhl were confiscated by the Soviets and one of the Sauer family arrested. To this day his exact fate is unknown. The head of production was put in a labour camp where he subsequently died. The rest of the family and some of their top engravers leapt at the chance to relocate to the west. The company was reestablished in Eckernförde in Schleswig-Holstein; West Germany where they had to start from scratch. They decided that the time-tested Model VIII would be the logical gun to restart production with, but the technical drawings were still in the East. So they acquired one, measured it precisely and made from this exact copies. In the mean time the East Germans under occupation were still making Model VIII's in Suhl. So they were coming from 2 factories. Later on the Model VIII's were even made in other countries (Italy and Spain) under licence from West-Germany, but always marked accordingly.

Initially after the war, the Allies forbade the use of the name Krupp on firearms made in West Germany. Such steel was instead marked Bochum Steelmaker's Association. I'm not sure if this restriction included the Krupp 3-ring symbol or for how long this regulation was in force. But it's perhaps another explanation for the use of the 4-ring symbol in Suhl post-1945, that it was to exloit the absence of the familiar and desirable Krupp brand on the wider market.

The American government put a 50% duty on East-German goods so I'm picking not too many made it to the States.