Thank you for your answer. In my case the problem applies to incoming external calls.
The snom phones should in the first place listen to the pbx-server.
Only if this server is disconnected they should automatically listen to the other identities.
For example, if an external call arrives on my sip-number 0123456789 and the pbx-server is connected, the phones should receive the call only via their first identity (the snom one-identity).
However, if the server is disconnected the phones may and should receive the call directly via their second identity, which has the same sip-number 0123456789.
The phones should not skip the server when receiving an external call.
They may skip the server for outgoing calls by choosing the second or third identity.