My phone is working again, yeah!
For the record, I went with both options in parallel.
@Freubert was so kind to send me a spare antenna cable of his phone.
While on the way, I also went to a repair shop to see, whether they could fix my original cable. They could not. However, they gave me a simple RF cable with MHF3-connectors. Interesing enough, this cable works, although it lacks the PBC attached to the original Fairphone antenna cable. Does anybody know, what this board is supposed to do? Apart from this suspicion, I could not find any information about it. The antenna seems to work perfectly fine without it, though.
Original fairphone cable with mysterious board in red frame. The antenna board on the right can be easly plugged off and on again.
Cable I got from the repair shop (similar) without mysterious board.
I’d love to learn, what the heck this PCB does. Is there a captain here?