Mac Mail into iCloud Mail?

I have a massive number of emails, arranged in mailboxes in Mail, from an Exchange account that I'm about to lose permanently, so I'd like to migrate everything into iCloud mail. I've set up that account, and it's working fine. But can someone advise me on how to get everything into the iCloud account? Can I use its folders in the way that Mail uses mailboxes, or is there a quick way to transfer everything perhaps?