Note The Hybrid Configuration wizard that's included in the Exchange Management Console in Microsoft Exchange Server 2010 is no longer supported. Therefore, you should no longer use the old Hybrid Configuration wizard. Instead, use the Office 365 Hybrid Configuration wizard that's available at http://aka.ms/HybridWizard. For more information, see Office 365 Hybrid Configuration wizard for Exchange 2010.
In a hybrid deployment of on-premises Microsoft Exchange Server and Microsoft Exchange Online in Microsoft Office 365, users can't use Outlook Web Access to move items between their primary mailbox in Exchange Server 2010 and their cloud-based archive.
This behavior is by design. You can’t use Outlook Web Access to move items between an on-premises Exchange Server 2010 mailbox and a cloud-based archive.
Use Microsoft Outlook to move archived items.