Assume that you deploy cross-premises archives with Microsoft Exchange Server 2010 or Microsoft Exchange Server 2013 on-premises. Exchange Server 2010 and Exchange Server 2013 have the following reduced functionality dealing with cross-premises archives.
For Exchange Server 2010
You cannot use Outlook Web App to copy or move items between on-premises mailboxes and online archive mailboxes.
For Exchange Server 2013 without Service Pack 1 (SP1)
You cannot copy search results from online archive mailboxes.
You cannot export PST files from online archive mailboxes.
Note There is no reduced functionality if you deploy Exchange Server 2013 SP1 on-premises.
Microsoft acknowledges that this is an issue in Exchange Server 2010.
To resolve these issues in Exchange Server 2013, install Service Pack 1.
Microsoft has confirmed that this is a problem in the Microsoft products that are listed in the "Applies to" section.