Hello. Have you looked into the IMAPSync tool here:
https://imapsync.lamiral.info/ This will migrate all of the mail. Do you also have calendars and contacts that you would need to move over?
Linda Pagillo
Mail's Best Friend
Email: linda.pagillo@mailsbestfriend.com
Web: www.mailsbestfriend.com
Office: 703.988.3606
Authorized Reseller of SmarterTools Products
Authorized Reseller of Message Sniffer