In a Microsoft Exchange Server 2013 hybrid environment, an administrator who uses ECP cannot grant full access permissions for an on-premises mailbox. This is because the administrator cannot select the mail user who has a primary mailbox that is located in Office 365.
This problem occurs because the remote mailbox is not in the selectable objects list in the DelegateFullAccess picker of the Exchange Control Panel (ECP).
Exchange Server 2013
To resolve this issue, install Cumulative Update 21 for Exchange Server 2013 or a later cumulative update for Exchange Server 2013.
Microsoft has confirmed that this is a problem in the Microsoft products that are listed in the "Applies to" section.
Learn about the terminology that Microsoft uses to describe software updates.