Boris Chertok, a Russian rocket designer, describes how Stalin received a request that British specialists be allowed access to a rocket test range in Poland in July 1944 from Churchill. In August Russian and British specialists made their way to the site where they discovered fragments of A-4/V-2 rockets. This marked the beginning of serious Soviet interest in the German Rocket Program.

Thanks to Von Braun the cream of German rocket talent and designs went to the US, however Chertok described in an interview decades later how he and Isaev a engine designer took over the Institute Rabe near Nordhausen in April 1945. Eventually the institute comprised about 1,000 people half Russian half German. With about 50 to 60 veterans of Peenemunde, mostly technicians but a few senior people including Helmut Grottrup and Kurt Magnus. The main job of the institute was to reconstruct the V-2 documentation that Von Braun had taken to the US. After the war several sites were taken over by the Soviets in their attempts to reconstruct the V-2 and understand how it worked.

In the fall of 1946 roughly 5,000 skilled Germans of all sorts were suddenly uprooted and taken by train to workplaces outside Moscow where most joined Scientific Research Institute 88 (NII-88). This institute, with Korolev in charge of Ballistic Missile development, concentrated initially on a Russian copy of the V-2 called the R-1with the first test launch in October 1947. Generally any designs for more advanced rockets that the German specialist put forward were not pursued and instead they were directed to help solve problems that the Russian designers had encountered. According to a CIA report of the time most new research that the Germans provided was in the area of instrumentation and testing equipment. In October 1950 all of the classified work done by the German specialists was cancelled, at least at NII-88, and they spent the next few years in a gilded prison working on their own projects. By November 1953 the majority of German specialists and their families went home with Magnus finally returning with his family in 1954. By then the Russians had got all they wanted and Soviet rocket development continued without any more German help.

Source Korolev, James Harford, 1997. Also see Rockets and People, Boris Chertok

Thanks for all the terrific answers. Headed down the rabbit hole.

They attempted many kidnappings on Kurt Tank, the designer of the Fw-190 and other aircraft many times while he was in Argentina.