An Office 365 ProPlus license is required for archive mailboxes. To verify the license type that is assigned to the affected user, open the Office 365 admin center, and examine the user’s license type. For more information about how to use the Office 365 Admin center, see Resolve license conflicts in Office 365 for business.
If a user needs full mailbox access to another user’s primary and archive mailboxes, you must grant them the Full Access permission. When they have the Full Access permission, automapping automatically displays the primary and online archive in Outlook Web App and Outlook. For more information about how to grant the Full Access permission, see Use the EAC to assign permissions to individual mailboxes.
If you assign full mailbox access to a specific set of mailboxes through a security group, the members of the assigned group won't see the mailbox automapped to their Microsoft Outlook profile. For more information about the issue and resolution, see the following Knowlesge Base article:
3190323 Mailboxes to which your account has full access aren't automapped to your Outlook profile
If the issue occurs for a user who is trying to access the Online Archive mailbox of another user, you can use the Support and Recovery Assistant (SaRA) tool to scan Outlook and review advanced diagnostics for known problems and details about the Microsoft Outlook configuration. For more information about how to use SaRA, see How to scan Outlook by using the Microsoft Support and Recovery Assistant tool.