It sounds like you're not wanting to use Migration Assistant to transfer everything over. In that case, we can do a relatively quick two step process outlined in the follwoing articles:
For ease of use, here are the pertinent insturctions from those documents:
You can export a mailbox to create a backup copy of it, so that later you can retrieve messages from the mailbox if you need to.
- Select one or more mailboxes, and then choose Mailbox > Export Mailbox.
- Choose a folder or create a new folder where you want to store the exported mailbox, and then click Choose. Mail exports the mailboxes as .mbox packages. If you previously exported a mailbox, Mail does not overwrite the existing .mbox file but appends a number to the filename of the new export to create a new version, such as My Mailbox 3.mbox.
Mail can import messages from other email apps or messages from mailboxes that you exported using Mail.
- Choose File > Import Mailboxes.
- Select the email app you want to import messages from. If you’re importing a mailbox exported from Mail, choose Apple Mail.
- Follow the instructions that appear onscreen.
Your imported mail is stored in a new mailbox called “Import.” To reorganize imported messages, create new mailboxes and drag folders and messages from the Import mailbox to other mailboxes. When you’re done, you can delete the Import mailbox.
If you don’t see your mailboxes in Mail, choose View > Show Mailbox List; empty mailboxes aren’t imported.