You can’t accomplish this, directly at least. Outlook express is intended to be a POP3 mail client, where as Outlook is not only a POP3 client, if configured that way, but also a IMAP4/MAPI client.
You CAN import your outlook express configuration into outlook, which will convert your contacts into outlook contacts. But you will likely need to setup outlook to be a MAPI/IMAP4 client (Via the “exchange server option” in “email account on the Outlook tools menu) then copy your contacts and E-mail up to the server.
From what it sounds like right now, when you connect to outlook you do not see your old mail, just messages that you have not recieved in outlook/outlook express. You will want to begin using outlook and telling it to deliver to the mailbox, rather than a PST file.