Hi Patrick,
It might well ‘work’ for P3i, but I can see 3 potential issues:-
First, you’d need to check that it’s a good match RF wise at the slightly different frequency (I would guess probably OK but you need to check the antenna specification or use an SWR meter designed for use on the correct 869.525 MHz frequency.
Second, some of the high-gain Chinese antennas are designed specifically for receive, and (IIRC) present a short circuit to a transmitted signal. (I would need to check this point).
Third, I don’t know whether the rules in Germany are any different to the UK, but over here we are limited to a maximum Effective Radiated Power (ERP) of 500 milliwatts in our part of the 869MHz band. We get away with using the ‘standard’ 7dBi antennas as they more or less balance out losses in the transmission system (coax, connectors, etc.), but using a 15dBi gain antenna - even if it proves a good match - could push the output above this limit. That is of course assuming the 15dBi rating is accurate.
So what I am saying is, it may well ‘work’ for P3i, but you would need to check these factors to ensure it works satisfactorily and legally.
It does look like it will be a useful antenna for FLARM reception though.
Best Regards
Peter