The university I am studying at recently migrated the mail system from Cyrus IMAP to Exchange Server 2007.
Unfortunately Mozilla Thunderbird does not work well with Exchange's IMAP server, unless you do some manual configuration:
First in order to make Thunderbird delete e-mails on the IMAP server correctly, you have to set the
mail.imap.expunge_after_delete option to true (see KB article).
Besides, you want to set the
mail.server.server#.trash_folder_name property to the name of the "deleted items" folder on the server (see KB article).
With this options changed, Thunderbird will interact with Exchange's IMAP server quite well.