The Soviet's didn't really know how to properly make use of "their" Germans though, at least for working on concrete projects. Only very few designs of German teams actually made it into production (like the turboprop engines used in the Tu-95: https://en.wikipedia.org/wiki/Tupolev_Tu-95), but the Soviets never trusted their Germans enough to really integrate them longterm with Russian teams, instead the goal was to extract the German knowledge as fast as possible and then "dump" them (most German engineers and researchers captured by the Soviets were allowed to return to Germany around the mid- to late-50s, leading to interesting, but ultimately doomed projects like the first German jet airliner Baade 152: https://en.wikipedia.org/wiki/Baade_152).
Meanwhile the "American Germans" were welcomed, decided to make the US their new home and contributed heavily to the US space programme.