I order two new - cheap - FTDI FT232RL USB-to-Serial Adapters on AliExpress.
After connecting, the first disappointment came directly. The Windows Device Manager displayed no COM port. Only a USB Serial Converter. The update of the driver brought no improvement. By coincidence I discovered the "Load VCP" option. After I activated this, the USB Serial Interface was displayed correctly.
Quickly the next disappointment came, both showing only gibberish.
I thought at first that the baud rate is incorrect, but with an older adapter it working correctly. On the FTDI website i found a tool called "FT_Prog". With these programming utility you can read and write the EEPROM for use with FTDI devices. After a few clicks I could see the difference:
Since I was not sure if there are other differences, I used the template function of the tool to copy the settings.