Export emails but keep them searchable
You can move the emails to a 'mailbox' which is only on your Mac.   The instructions here assume you have the latest version of macOS and Apple Mail, but older versions are much the same.

In Mail's sidebar on the left you should see &quot;On My Mac&quot;. With the
mouse, hover, click on the disclosure triangle to show the mailboxes
(folders) inside &quot;On My Mac&quot;.

Create a new mailbox (folder) by clicking on the + symbol.  You may
want to create multiple mailboxes to keep your emails organised. You
can even create a tree structure if you want.

Then just drag and drop (with the Command key pressed) your old
business emails from the external mailboxes into your new mailboxes
within &quot;On My Mac&quot;. The command key ensures that you do a copy (not a
move) as you probably don't yet want to delete them from the external
service.

Alternatively use 'Copy to' from the Message menu.

You can now disconnect from the old mail services.


The emails will be indexed (it will take a little) and be available to Mail's search.
Because the emails are now stored just on your Mac, you become responsible for ensuring your backups are sound.