Downloading the mailbox to a PST

If you have delegated permission to access a user's mailbox, you can move or copy its content to a PST using Outlook's native archiving feature. We don't generally recommend this approach, because it is labor intensive, consumes a lot of bandwidth, and ties up a workstation for long periods of time. That being said, many Office 365 customers have gone this route either due to budget constraints or simply because admins are more familiar with this method than with other options.

It's important to point out that backing up Outlook is not going to preserve files in OneDrive for Business. Other steps would be required to protect those assets.