Apple Mail makes it easy to set up an IMAP account alongside your POP account. And once that is set up, you can drag and drop your email into the IMAP account and it will be imported.
IMAP works differently than POP because it is constantly in contact with the mail server and all your mail stays on the server unless you explicitly delete it from Apple Mail. That means you can keep all your email in sync between Gmail and several different laptops.
Some of the steps below may not be exact, because they may vary slightly between different versions of Mail. But generally speaking, this is the way it goes:
First, get ready to set up a new IMAP account in Apple mail. The first thing you need to do is go to Gmail and disable POP and enable IMAP. Those settings are in “Settings” under the gear symbol at the upper right hand part of the Gmail screen. Inside Settings is a tab labeled Forwarding and POP/IMAP, and in that tab you can disable POP Download and enable IMAP Access.
Once you’ve enabled IMAP, go back to Apple Mail and start a new account. Under the “File” menu, go to “Add new account…” or go to Preferences and in the Account tab click on the plus sign. This will open a window with a drop down for the type of account, so select IMAP.
You’ll need to enter the full account email, full account name and password. Apple Mail will check the connection to Gmail and let you know if anything is amiss. Once the connection is good, Mail will show the new account as a new box in your Inbox, as well as new boxes in Drafts, Trash, etc.
You can go back to Gmail and go to the Labels tab and select the different boxes you want to appear further down the list.
If you have a lot of mail, it wil take a while for Gmail to sync everything up. And when that is done, you can drag your sent POP mail into the Sent mail folder for Gmail and those messages will be uploaded into Gmail.
Once you’re done with moving mail from POP to IMAP, you can either delete the POP account or simply make it inactive.