I know it's an old puzzle, but since we try to maintain the highest possible level of accuracy at AP, I feel that a bit of clarification is in order.
The car is in fact the Lux-Sport (PZInż. 403). At least two chassis were built in 1930s, one fitted with bodywork the other only as a rolling chassis. The latter survived to this day and can be seen in Warsaw in the Technical Museum. The car was intended for production in 1940, when the licensing agreement with Fiat was to end.
PZInż. (Państwowe Zakłady Inżynieryjne = State Engineering Factories) were created in 1928 from the earlier CWS company (Centralne Warsztaty Samochodowe = Central Car Workshops). Later also truck producer Ursus was merged into PZInż. The CWS make for passenger cars was retained until 1932, and the Sokół make for motorcyles until 1939. Since 1932 a new factory produced license-built Fiats (the original Polski Fiat, not to be confused with Polski Fiat from 1960s-90s). PZInż. was also responsible for designing and producing military vehicles (they also made some navy vessels) as well as agricultural equipment.
The Hanomag link is only speculative - it is assumed that German spies stole the plans from PZInż. and used them to design the body of a new Hanomag model.
