He wrote, too, that the installation of compat-wireless (unfortunately,
he didn't told me which version), didn't changed the situation.

I attached for him the output of
options iwlwifi debug=0xffffffff

The last part of it:

what about the logs *before* that?

[  675.594758] iwlwifi 0000:03:00.0: Failed to run INIT ucode: -5
[  675.594863] iwlwifi 0000:03:00.0: Unable to initialize device.

I hope this debug output can help you to find the problem!

Sorry, it can't