In Microsoft Office 365 Dedicated, you have Send As permissions for a newly created mailbox. You try to send mail from this mailbox by using an installation of Microsoft Outlook that's set up in cached Exchange mode. In this situation, you receive a non-delivery report (NDR) that resembles the following:
You can't send a message on behalf of this user unless you have permission to do so. Please make sure you're sending on behalf of the correct sender, or request the necessary permission. If the problem continues, please contact your helpdesk.
However, you can send mail as the user in Microsoft Outlook Web App (OWA) or in a version of Outlook that's set up in online mode. Additionally, this issue seems to resolve itself after several days.