Send As An Alias In Microsoft Office 365
Unfortunately, in Microsoft Exchange 2010 and therefore Office 365, you are unable to send from any email address other than your primary one, even if you can receive email from multiple email addresses.
If you have ever tried to do this, it is likely you have received the following error:
"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."