Q: How can I move emails from an old account before closing it?

Any reply would be more direct if you had told us what sort of account (provider, POP, IMAP) you want to close and what you will be using for sending and receiving email in the future.

But anyway here is one approach.

1) I'm going to assume that you are using Apple's Mail application. And that you have an IMAP account. If you have a POP account then the steps below shouldn't be necessary.

2) Show all mailboxes

3) Show the "On my Mac" mailboxes

4) Maybe make a new mail folder, something like Saved Mail from XXX account

5) Select all of the mail from the Inbox, Sent Mail, other folders from XXX account

6) Move them (menu bar Messages label) and select Move to then select the destination folder in On My Mac.

7) Now, with luck, all of your email messages are archived on your Mac.

Many of these steps have sub-steps. Write again for further clarification and to supply more details.

Good luck,

W R Glendon