How to manage AOL and Gmail accounts in Apple Mail?

There are 2 email accounts in Mac Mail, 1 AOL and 1 Gmail and want to terminate the AOL account.

Can I MOVE the AOL emails from their respective (inbox, sent etc) to the Gmail account (inbox, sent etc), terminate the AOL account and expect to be able to continue to view all of the moved emails from AOL in Gmail?

I would certainly archive all of AOL as a backup.

But would this work just by moving the emails to Gmail regardless of archiving?

Also, would like to know if this would work on iPad A16 chip as well as 2019 iMac.

Thanks

[Re-Titled by Moderator]

Original Title: Apple Mail with AOL and Gmail accounts