Question : e-mail sharing w/Outlook Express

I have a desktop(host) which is networked to a laptop(client). The desktop is sharing a cable internet(Comcast) connection. Both computers use Internet Explorer 6 & Outlook Express 6.  The shared internet connection works just fine.  My question concerns sharing of e-mail.  Is it possible for the client computer to share e-mails RECEIVED by the host computer?  

We have performed the following tests.  An e-mail sent by the client computer to our (both host & client) e-mail address was received by the client computer after pressing the SEND/RECEIVE button.  It was not present on the host computer.  An e-mail sent from an outside source was received by the host computer but not by the client computer.

Thanks for any & all help.

Answer : e-mail sharing w/Outlook Express

computer name, not drive label.