If you want to back up the message folders locally (in addition to keeping them on the server), you can automatically move or delete older items with AutoArchive or export the items to a .pst file that you can restore later as needed and use by importing. Select File > Open & Export > Import/Export. Select Export to a file, and then select Next.
You can export your Outlook.com mailbox to a .pst file using new Outlook for Windows or classic Outlook for Windows, or export to a .olm file using legacy Outlook for Mac.
Export Outlook email, contacts, and calendar to move them to another computer or so that you can make a backup of your information.
Export emails, contacts, and calendar items to Outlook using a .pst ...
Training: In Outlook, you can export your contacts into a .pst file to make them portable and easier to move. Watch this video to learn how.
If the Import/Export option isn’t available in Outlook 365, it usually means you’re using Outlook on the web or your admin has turned off that feature. Here are some ways you can still export your emails to your hard drive: If you have the Outlook desktop app, the easiest way is to use the built-in export tool.
How to export emails in outlook 365 to hard drive - Microsoft Q&A
Summary: Learn how administrators can view, create, modify, delete, suspend and resume requests to export mailboxes to .pst files in Exchange Server 2016 or Exchange Server 2019.