Archive old mails to my computer using mac mail application.

Create Mailboxes in the On My Mac section.

Then, drag emails from the server mailboxes into the On My Mac mailboxes.

You could create a Smart Mailbox that would find all emails older than a given time. You could then Select all of those and drag them into the On My Mac Mailboxes.

If you need to organize them more than just one folder, you could create several Smart Folders that would filter by other criteria.

You could also make rules that would move the older emails into the desired On My Mac mailboxes.

The Rules and Smart Mailboxes use similar criteria to find emails, but you could use a Smart Mailbox in conjunction with a Rule to move the messages.

You would have to run the Rules manually as they only work automatically on messages that arrive into the Inbox, so those would never be old.

I just want to make sure you understand that the Smart Folders do not move anything. It will just find all of the emails, showing them in one window where you can then select all and move to another real mailbox.