You can set up your fastmail-account in your Tbird as POP or IMAP POP setup will pull your emails down to your pc (usually deleting them from fastmail-server) IMAP setup will download headers and sync between server and client (Tbird) That way you can access the same email from different devices (like pc, mobile, tablet, web mail ....) Here is Fastmails settings https://www.fastmail.com/help/technical/servernamesandports.html For backup you can copy those into local folders or export them.