A Brief History of the Marque
1934-1945 Berlin-Suhler Waffen- u. Fahrzeugwerke (Simson & Co.) BSW, Suhl
1936-1945 Gustloff-Werke Waffenwerk, Suhl
With the assumption of power by the Nazis in 1933, the Jewish family Simson was expropriated in a show trial and sentenced to a payment of 1.75 million Reichsmark. Automobile production was discontinued in 1934 and the company was renamed Berlin-Suhler weapons and vehicle plants. The new BSW as well as the Gustloff-Werke in Suhl became a focus operation of German armor. From the mid-30s the former Simson works, now BSW Gustloff, resumed production of motor vehicles, among them the BSW 98, which was built until 1940.
In 1939 Martin Stolle designed a lightweight motorcycle known as Sursum equipped with a Sachs 98cc two-stroke which was manufactured by Gustloff.
After 1945, the Simson factory was taken by the Soviets and became (SAG Awtowelo AWO), later integrated with the IFA conglomerate. It was not until the early 1960s that the name Simson was revived in the GDR. 
Notes. 1. Interesting take on the "Jewish Question" : jewishvirtuallibrary.org/joseph-stalin
Sources: GTU Oldtimerservice, et al.