[till]

Here the solution for this issue:

The reason for your problem was that the mailbox was disabled in ISPConfig.

There are 3 checkboxes in the mailbox settings. These were your settings:

[ ] Enable Receiving
[ ] Disable Imap
[X] Disable Pop3

I changed them now to:

[X] Enable Receiving
[ ] Disable Imap
[ ] Disable Pop3

And the mailbox works now. The settings that I have done now are the defaults when you create a new mailbox.