The external postmaster address is used as the sender for system generated messages that are sent to users outside the organization. All domains which are not in the accepted domains list are treated as external domains. Check one of my previous articles to know more about setting the postmaster address in exchange 2007, which can be done only using the shell.
While the same method works for Exchange 2010, the product group has exposed the option in GUI as well. Hence, for admins who doesn’t like fiddling with powershell, navigate to EMC -> Organization Configuration -> Hub Transport -> Global Settings tab.
Right click Transport Settings and select properties. Type in your postmaster address and click OK.
One more option exposed in 2010 console!
