Best solution is to export your email database, that way your emails also remain safe and secure. Here's the procedure:
Export mailboxes
Select one or more mailboxes, then choose Mailbox > Export Mailbox.
Choose a folder or create a new folder, then click Choose.
Mail exports the mailboxes as .mbox packages. If you previously exported a mailbox, Mail doesn’t overwrite the existing .mbox file; it creates a new .mbox file, such as My Mailbox 3.mbox.