Digging a little deeper with the latest information brought up the following: "Fahrrad- und Metallwerke L. Bauer & Co.", founded in 1911, were located in a place called
Klein-Auheim, a small town in the wider area around Frankfurt with around 6.500 inhabitants at the end of the sixties. Kolbe was located in same town. On old webpage of unclear trustworthyness said that a daughter of Mr. Bauer married a Mr. Kolbe which then probably led to the bike brand Kolbe which probably was a subbrand of Bauer with bikes coming from the same factory. Bauer was a very famous brand for bicycles (
in 1947 they build already 1000 bikes per day), Kolbe not so much (more of regional fame, I come from roughly around that region and know the brand from back then; it was not a big brand) and "Hesswinkel" seems to be either a subbrand of Kolbe or rather a model of that brand. So I'd assume that Kolbe possibly either bade engineered Bauer bikes or acted as a subbrand for i.e. slightly cheaper bikes with mainly regional distribution.
Coming to the dates: Bauer went insolvent in 1968, the year your bike was given to it's former owner. Bauer got sold to Rowenta and stopped making bikes, Kolbe kept existing, probably badge-branding bikes from other manufacturers. But this was after your bike was made. In
Bauer's wikipedia entry there is a picture of a "Bauer sport" between 1961 and 1968 which in many ways shows similarities to your's:
(Von Lothar Spurzem - Eigenes Werk, CC BY-SA 2.0 de,
https://commons.wikimedia.org/w/index.php?curid=61454195)
It is however not completely original, looks to me like early 60ies with some more modern componets and components like the front brake are of higher quality. However, at that time the choice of components were far more limited than today so similarities may just be a coincidence, not necessarily a correlation.