OK, I found it out. ISPconfig maps the email address from the squirrel login form to the username expected by postfix by means of a file called /etc/postfix/virtusertable. Here, I then recognized, there was an error done by myself: I created a web as subdomain, so I had to input firstname.lastname@example.org as username in squirrel, and the mapping file did the rest well. If I typed only the username, squirrel has completed this by the "@dom.tld" but for this there was no mapping entry in the virtualusertable und the logon failed.
This had confused me!
So thank you again.