I had this question after viewing Sending message failure
I've tried Blue Street Techs accepted solution of removing the Save As permissions and adding them back, but I'm still getting the error message :
This message could not be sent. Try sending the message again later, or contact your network administrator. You do not have the permission to send the message on behalf of the specified user. Error is [0x80070005-0x0004dc-0x000
the problem account is a shared mailbox. Is there something that I'm missing?