Sometimes moving mail from one Mac Mail to another can be a pain. Here is a quick guide that should overcome most common problems, and lets you monitor the progress of your exports/imports.
This is the process I followed which appeared most successful when migrating 20 Mac Mail mailboxes to new Macs.
Step by step guide:
1) Firstly the Activity Monitor should be open, when inside the Mail app, go to Window > Activity (this is important and allows you to tell when the mail export is finished or import is complete). I had issues with this on older versions of Mail Mail, not showing correct statistics. You may also wish to open your User > Library > Mail > Folder and monitor the size of your MBOX files by right clicking > Get Info and monitoring the size as you import mail back.
2) Select your mail folders, e.g. Inbox, I advise doing them one at a time, Inbox first, then Sent Items. Click on the Mailbox menu and select Export or Archive mail. Choose the folder and press export. Keep an eye on Activity window to see completion, or do the Get Info to monitor file size by right click.
3) To import, if the mailbox is large, 4GB+ importing it’s important to keep an eye on the Activity window or size of the MBOX file in your library as above to know it’s working correctly. Click the File menu and select Import Mailboxes, select your MBOX backup and choose Apple Mail as the method of importing. In some cases the method ‘Apple Mail’ didn’t work for me, and when this happens and it locks up or freezes for hours, I recommend using MBOX as the import option, and browse the Apple mbox file, and select the file called ‘mbox’ within the Sent Items or Inbox files.
4) Once successfully imported it’s important to not drag and drop the imported mail, as this tends to screw up file indexing and mail can get lost if it’s thousands of messages. The best method is to select all mail from the import folder from the Edit > Select all menu, then right click and select Move Mail to > Inbox or Sent box, depending on which you are importing. Mail will vanish from the ‘import’ folder, this is normal. Please allow several minutes for the mail to reappear in your Inbox or Sent Items folders. You can monitor the inbox.mbox folder or Sent Messages.mbox folder from your user > library > mail folders by right clicking and doing ‘Get Info’. This will show you the mbox file increasing in size. When it stops you know all your mail should be imported.