Hello and good afternoon! This is an excellent question and I'd be happy to provide some guidance. The best way to migrate data from an existing CPanel server is likely using Settings>Connectivity>Mailbox Migration as this will allow you to leverage IMAP to sync the entirety of the account mail data into the new user's account in SmarterMail.
If you need an automated unattended solution I recommend checking out IMAPSync/IMAPCopy. These utilities allow you to essentially script an IMAP migration between the old and new server for all accounts simultaneously.
Alternatively downloading the email data into an email client, then uploading it to the new SmarterMail account should also suffice. I hope this helps!
Kyle Kerst
IT Coordinator
SmarterTools Inc.
www.smartertools.com