Further experimenting with another client was successful.

So, the example from my previous post is working, thank you all. But:

As there's still the possibility that my two hardphones have the same strange behavior - is there a way to get protocol information to detect WHY some machines behave differently? May be there are some options with the session bind to make the other phone happy to answer?

The non-working software was CSipSimple version 1.02.03, Android. The working kind was Zoiper 1.19.7 Android.