Exchange online archive file management help

NTA-Mark Just to clarify, you mention Exchange and you mention Office 365. They are essentially two different things. When we use the term "Exchange" we are normally referring to a physical on premises server installed and managed by the customer. Exchange Online is Microsoft's cloud service that is managed by Microsoft and is sometimes referred to as "Office 365". I'm going to assume that the user's mailboxes are in Exchange Online (Office 365).

Depending on the licence that your users have, a user can have both a mailbox, and an online archive. Both of these may have size restrictions, again depending on the license. If the user has both a regular mailbox and an online archive, they will see both when connecting via Outlook and via OWA:

This really isn't something that an admin can manage as it's an issue with the amount of data the users are storing in the archive as the size of the archive has exceeded the licensed limit. What the users need to do is open the archive and remove unwanted messages. Having the user remove attachments and storing them in OneDrive may also significantly reduce the archive size. Users can also use the Outlook client to export messages to a file for storage elsewhere, but then you have an issue with where you store that file and the fact that the file may be a security issue (anyone who gets that file can open the messages in it) so it's not something I recommend.