@Steve: thanks a lot!
What I have done so far: switched on B&O TV, PUC downloaded (PS4 IR Dongle), connected the IR eye of the B&O Avant to the FLIRC, plugged it into the computer, programmed the keys on the Beoremote one. All keys were successfully recorded. Plugged in the FLIRC with the IR eye into PS4. Just doesn't react at all on PS4. Looks like that PS4 is not recognising the FlIRC.
When I open an editor on the computer, at least the "enter" button is working... so, some keys are programmed to the FLIRC.
Any idea?
Michael