Store attachments locally in Mail.app when using IMAP
You will want to make a new mailbox with storage only on the Mac or use the Archive function in Mail to archive an entire folder/mailbox.

The built in help will guide you through the Archive path.

I just make folders "On My Mac" with the year, and then make Q1, Q2, Q3, Q4 folders inside to keep each relatively small - you might only need one folder per year or one folder.


Once you move the message and are comfortable that it's on your mac with attachments intact, delete the original message from IMAP and your quotas will be happier.