Mac Mail in macOS Sierra allows you to export the mail messages of a mailbox in an email account as a backup/archive as well as the ability to re-import that mailbox content into another email account.
Exporting a Mac Mailbox
In Mac Mail choose your mailbox to export in the mailboxes column via the Mailbox Menu and choose ‘Export Mailbox’, navigate to a destination folder and export. The resulting export will be named similar to ‘INBOX2.mbox‘ with differing increment numbers.
Mbox is a generic Linux format for storing a number of email messages.
Importing a Mac Mbox Mailbox
Importing is easy, you don’t select an email account initially, you bring in the mailbox as a new mailbox and then manually move the mail where you need it to go.
Import that mbox format into another mailbox first, go to the File Menu > Import Mailboxes and navigate to where the exported mbox folder is and choose that to import, what happens is that it is stored as a new mailbox in the mailboxes column with a generic name like “Import-2”
Now all you have to do is locate the mailbox see the contents and click and drag the messages to a new mailbox destination.
That’s it, the mbox format is easily transferred between multiple mail accounts.