Almost everything related to moving/converting mail accounts can be done using the dsync tool. It can do either one-way synchronization or two-way synchronization of mailboxes. See:

doveadm help sync


doveadm help backup

for more information. Also describes how to migrate mails from another IMAP/POP3 servers.

Mails can be also imported to an existing mailbox using:

doveadm  import

The new mails will be appended to their respective folders, creating the folders if necessary. It’s also possible to give a prefix for the new folders, such as “backup-restored-20140824/”.

Mails can be also continuously replicated between two Dovecot servers using the replicator service. See for more information.