Is there a setting to allow "Delivery Failure" messages to be generated for mail sent from a domain alias email address to an invalid recipient?

 

For example when a message is sent from user1 at the original domain name to an invalid recipient we receive a "Delivery Failure" message from "System Administrator." However, when an email is sent from user1 at the alias domain name to an invalid recipient we do not receive the "Delivery Failure" message from "System Administrator." Instead we receive the delivery failure message from recipient server if it exists. The failure messages may vary from party to party so the system generated "Delivery Failure" messages are much more useful for automation.