After I connected the printer to the cable adapter to a USB port (without a hub in between), teamed up once nothing. The printer could not be seen in the printer list in the Device Manager.
Did then once tried rumgerätsel and several USB ports, run by the HP Printer diagnostic tool (the program recognized the printer does not also). Then I had the idea time to look in the Device Manager under "Printer" and behold, he was there and installed. In the normal printers list he is still not (because where one specifies the default printer), but never mind. One can only not set as the default printer holding it. Word, Excel etc. "see" the printer, so you can select it.
So everything is ok in the end for an investment of less than 4 euros.