For some clients who currently use Microsoft Hosted Exchange accounts with the In-Place Archiving feature enabled, the In-Place Archive Mailbox is not appearing in their full-version of Microsoft Office Outlook 2013 software connected to their Exchange account. Users can see their Archive in Outlook Web App, just not in the full-version of Outlook 2013.
The Microsoft Hosted Exchange service does in-fact support this feature, but the In-Place Archive feature requires specific Outlook licenses. For organizations using Microsoft Corporate Licensing Agreement or Microsoft Service Provider Licensing Agreement (SPLA) versions Microsoft Office Standard 2013 does not support the In-Place Archive feature, while Microsoft Office Professional Plus 2013 does support this feature.
This is not a Microsoft Hosted Exchange feature or licensing problem.
This is a Microsoft Office Outlook 2013 version issue.
Here is a link to the feature comparison of the Exchange Online plans:
Here is a link to the Outlook license requirements for use with Microsoft Hosted Exchange Online features: