Outlook Email Backup

Yup - like this.

https://support.microsoft.com/en-us/office/back-up-your-email-e5845b0b-1aeb-424f-924c-aa1c33b18833

There is, but it depends on your environment (and I'm assuming your account has already been deactivated).

In Outlook, go to File, Account Settings, Account Settings. Click on the Data Files tab.

If your email address has a check next to it (meaning it's your default mailbox) and the Location is set to "Online" then you're SOL. You'll have to get with whoever was managing the mail server to get a copy (if they still have it).

If the Location path ends in an email address (ex: C:\users\yourusername\appdata\local\Microsoft\Outlook\you@yourbusiness.com.ost) that's an OST file (it's a cached version of what's on the server). You'll need to either create a PST then migrate everything to it or export your mail to a PST.

To Export an OST to a PST, in Outlook go to File, Open/Export, Import/Export, choose "Export to a file, choose the .pst option, then choose the entire mailbox (entry at the top of the tree). After this is done, go back into File, Account Settings, Account Settings then your Data Files tab and make that PST your default mailbox (so everything is delivered there from now on).

If the Location path ends in ".pst" and that location is the default (check mark is next to it), then you already have it all. You should be able to just open Outlook and access those files. You can also use the above directions to find where your PST file is located, then copy it to a USB drive for use on another computer.