Log into your new cPanel account.
Create Email accounts that you intend on transferring.
Now you will want to connect your FTP client to the old cPanel account.
Find your mail files and folders and download them to your local machine.
Disconnect your FTP client from the old cPanel account.
Now connect to your new cPanel account through FTP.
Find the Mail directory
Upload the downloaded mail files and folders from the old cPanel account to the new cPanel account.
Note: This can be useful when migrating hosts, migrating just email accounts, or simply changing one users email under a particular cPanel account to another.