Not quite true.
The MiG-9 was first flight on April 23, 1946, engine reverse engineered BMW 003. Yak-15 was first flight on April 23 1946, engine reverse engineered Jumo 004, La-150 first flight September 11, 1946 engine German Turbojet. The Sovejet Jet engine proposed was a Lyulka TR-1 with a first run on August 9, 1946.
So the development of jet engines and Jet airplanes were based on the German technology that were captured in east Germany, mainly the Junkers factory and jet development teams. The production of the Jumo 004 continued under supervision at the German plants by USSR.