I've transferred my accounts, however, email has been delivered to the source server before the DNS was updated.
Unfortunately, there is no native option to transfer only mail from one server to another. Instead, the full cPanel account will need to be transferred using the WHM Transfer Tool. Transferring the account post the DNS having been updated will ensure all mail is appropriately synced to the new server.
Alternatively, you may follow the instructions provided within this article in order to sync the mailboxes using Imapsync.