Recently I have been working on Microsoft Exchange Send as permissions with shared mailboxes.
When setting the Send as permission in Active Directory you have to select the mailbox you want to configure and go to the properties of the account. Select the Security tab and either select or add the name or group. In the permission pane scroll down to Send as permission and check the Allow box then click Apply and OK.
For the changes to take effect and to get this to work in Outlook 2013, I had to restart the Outlook session.