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Exchange 2010 - proper configuration of SMTP

I have just installed Exchange 2010 in my home lab and now struggling with some SMTP configuration issues.
I am able to send emails between the members of the Exchange organization, but unable to send emails over the Internet.
My first trouble comes in the following form:
when I attampt to send an email to an internet recipient, it comes out this way:
 From: eugene@devlab
It should read From: eugene@devlab.us
What are the exact steps for me to make this change?

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