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So, is there a way for dovecot-{lda/lmtpd} to accept "user1@mydomain.org" but checks for "user1" in the user DB?

Try username_format=%n so dovecot uses the username only: http://wiki2.dovecot.org/Variables

passdb { driver = passwd-file args = scheme=PLAIN username_format=%n /etc/dovecot/mypasswd.file }

Great! I did not think about that, but this solved this issue :D Thank you a lot.

And I was now able to solve also my further issues. So I am prepared to try again to switch :)

Have great day!

Matthias Hofer