Can cPanel restore or transfer MBX mailbox files from my DirectAdmin, Ensim, or other third-party control panels?
cPanel does not convert MBX mailbox files when transferring from a third party control panel.
In order to transfer messages in the MBX format, you must use a third-party tool such as ImapSync.
We have a guide that explains the process of syncing messages with ImapSync here:
How to Sync IMAP Inboxes with IMAPSync