How to burn time! Ok, I found the problem. The contact was imported via VCF file with:
...
TEL;CHARSET="UTF-8";TYPE=CELL,HOME:+4912345678901
...
This seems to not be handled very well by jolla-messages application.
When doing the import as
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TEL;CELL;HOME:+4912345678901
...
I am able to write a message now!