Explicitly grant BESAdmin service account permission to send as a mailbox owner.
Follow these steps:
1. Start the Active Directory Users and Computers management console.
2. On the View menu, make sure that the Advanced Features option is selected. If this option is not selected, the Security page will not be visible for User account objects.
3. Open the properties of the user account that owns the mailbox.
4. Click the Security tab.
5. If the BESAdmin is not already in the list of group or user names, add the BESAdmin account that should have the Send As permission for this user.
6. In the Permissions box, click Allow for the "Send As" permission for the appropriate account.
7. Click OK.