If by the West, you mean the United States and West Germany, the answer is remarkably few. After World War II, Germany was divided between the Allies (Britain, France, and the United States) and the Soviet Union. In Allied sectors—which would eventually become West Germany—the Office of Military Government, United States (OMGUS) was doing everything it could to hobble German film production, largely at the behest of the Hollywood studios (see Theaters of Occupation: Hollywood and the Reeducation of Postwar Germany by Jennifer Fay for an in-depth study of this). In the Soviet sector, which would eventually become East Germany, the Soviets were anxious to start making films again thanks to the influence of the Russians, who considered cinema the most powerful medium for enlightening people to the benefits of communism. It didn’t hurt that that the heralded UFA Studios in Babelsberg—the birthplace of classics such as Metropolis (1927) and The Blue Angel (1930)—were now in the Soviet sector.

At first, the U.S. ignored the films coming out of East Germany’s newly formed DEFA Studios, but when these films started showing up in theaters in South America (New York Times, October 5, 1947), officials in the United States went nuts. By this time the U.S. was in the middle of the Red Scare, fomented by the House on Un-American Activities Committee (HUAC). A month after the New Times article about the distribution of DEFA films in South America, Republican congressman and HUAC member Karl E. Mundt was given several pages in the New York Times to complain about the communist influence in Europe and outline a new plan to combat it (New York Times, November 9, 1947). Efforts were made to actively discourage the distribution of East German films in both the United States and West Germany. Without any official ties in the US―which did not recognize East Germany as a legitimate state until the seventies―getting films over here was difficult. In West Germany, a board was set up for the express purpose of banning any East German film that contained even a hint of socialist sentiment, and a doctrine was created that threatened to sever ties with any country that even acknowledged the existence of the GDR (the Hallstein doctrine).

The exceptions to this were the East German fairytale films, which were allowed to be imported worldwide. The Golden Goose (1964), for instance, was distributed in the United States by K. Gordon Murray Productions, a company that specialized in purchasing foreign fairytale films on the cheap and dubbing them (rather poorly) into English. And in 1964, The Singing, Ringing Tree (1957) was broadcast on the BBC, terrifying an entire generation of British children.

Things didn’t really loosen up until Erich Honecker took over as General Secretary of the Central Committee (the top position in the GDR) and started actively seeking better relations with West Germany, which eventually led to both countries being admitted into the United Nations in 1973. A couple years later, East Germany received its first foreign film Oscar nomination for Jacob the Liar (1975).

Even so, the distribution of East German films in the West was spotty at best. West Germany started showing more of the films, but there were very few American and British companies that were willing to put in the effort to dub or subtitles the movies of East Germany. As a result, the film so East Germany have received far more screening in the United States since the dissolution of the country than they ever did during the country’s existence.