MS Outlook: additional mailboxes are not synchronized to an OST file

Initial setup

The client computer is outside the domain and connects to MS Exchange 2010. The user has been granted Full Access permissions to additional mailboxes.

Problem

The connected mailboxes are not synchronized to the local OST file; only the user's own mailbox is synchronized. As a result, the user cannot see mail in those mailboxes while working offline.

Solution

Enable the Download shared folders option in the Outlook connection settings.