Further investigations:
I tried to register the handset, this time looking carefully to the numbers shown:
I recognized the Beocom base PSTN number > entered 0000 as pincode > got error.
Reset the handset. disconnect the PSTN Base PSU.
Tried to pair with the Internet box:
Saw a different PSTN number > entered the known pincode > Got error again.
Reset the handset, tried again with Beocom PSTN base after it had no power for several minutes. Got same error as above.
In the administration page of my box a DECT1 handset shown briefly.
I believe the handset is faulty like he can see bases but is unable to communicate with them.
Does it make sense?