Hi Luca,
Short answer is no. The flood illuminator is keyed to the logic board using a proprietary encryption algorithm that only Apple has access to, so they are the only ones who can replace that part and have Face ID continue to work. If you find a sufficiently talented repair person, they can move the paired components to a new flex cable or sometimes even reconnect the existing cable itself, but it takes someone with very specialized skills and equipment; most of your average repair shops couldn't do it.
Outside of finding someone capable of doing that repair, the only other option you have is to pay Apple for a full screen replacement. Their replacement screens come with the earpiece speaker already attached and the last step in their repair process is to run the "calibration procedure" to pair the earpiece speaker assembly to the logic board, as well as setting the MtSN data so True Tone will still work.