When migrating from one cPanel server to another cPanel server it’s easy and automatic, but if you need to migrate your email from an old host without cPanel it’s not automatic, but there’s still an easy way to do it with this tutorial.
First, download and install Thunderbird on your computer if you do not already have it. Thunderbird is a common popular desktop email program.
Second, you will have to add 2 email accounts in Thunderbird, the old email account and the new email account. When adding the old email account, set the mail server to the old server’s ip address, and in the Description field type something to indicate it is the old account. Similarly, when adding the new email account, set the mail server to the new server’s ip address. I recommend using the IMAP protocol for both the old and new account.
Lastly, now with both accounts loaded into Thunderbird, click on the old account from the left panel, and on the right side where all the emails are listed, just drag & drop the emails into the new account’s folder on the left panel.
There’s no limit to how many you can move at once, but from my own experience in doing this, you should only move small amounts of emails at a time.