Using Outlook 2010--Sent of behalf of doesn't show up when sent to external emails like Gmail. It just says the name of my boss. It shows up on emails sent to people on the network. How do I make it appear on all emails, not just the ones on Exchange? 

How do I make it appear on all emails, not just the ones on Exchange? 

By submitting it as a feature request to the developers of those other mail clients :-D
There is nothing you can do about it from an Outlook/Exchange perspective.

I have tested as well, and the same results. This is not depend on us as Roady said :) 

regards,

Csaba