To add an email alias, please see this article Adding email alias in Google Apps

If you are getting this error when sending email to the email alias address:

Delivery to the following recipient failed permanently:

 

    --- email alias address---

 

Technical details of permanent failure: 

The partner did not specify the domain to relay the emails

Please check if your users have the correct email routing enabled. Do the following:

1. Go to admin.google.com
2. Select 'Users' and on the next page select the account with the email alias you had attempted to send the email to.
3. Select 'Account' and scroll down to 'Email routing'.
4. Ensure that 'Google Apps email' is selected as a destination.
5. If you are having issues enabling Google Apps email routing , please contact support.