you COULD use imapsync actually… but it failed me with some obscure error.

rsync is NOT a good idea… because dovecot/thunderbird/icedove does not rebuild index files/folder structure.

the solution is actually simple: use thunderbird/icedove your mail client!

  1. create same mail account on new server as on old server
  2. add old and new account inside thunderbird (you can use IP addresses if the domain is already pointing to the new server)
  3. drag and drop the old mails-folders from your old account to your new account
  4. wait… all mails get downloaded locally from your old account and then uploaded to your new account, depending on your internet/amount of mails/server-speed this could take a while.

HINT: You may need to do this serveral times (first it just copied/created the folder structure, but not copied the mails)

so i had to manually drag and drop (Ctrl/Strg+A = select All really helps) all mails folder-by-folder from old server-account to new-server-account.

BTW: SERVERFAULT.COM SUCKS! i already know they will remove my answer. so here is the screenshot: