I just set up and o.com account.  I downloaded the connector, rebooted etc....

I can send from O2003 but all replies are only received in o.com ONLINE. 

Win 7 Pro

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So, I send an email from outlook 2003 using my outlook.com email address. 
The recipient receives the email.
They reply.
The email is received @ outlook.com but not in outlook 2003.