SMTP is not the protocol for receiving mail from a server, but for sending new mail. So at question here is whether your mail server is being accessed as a "POP3" or "IMAP" server. If the mail is being downloaded as a "POP3" server, then it is quite possible that the mail does not remain on the server after you download it to the mail client program (in this case Outlook).
In order to read mail from multiple computers you need to have an IMAP mail server, and your mail server needs to be configured to provide IMAP access to "ALL mail" (in Google when you turn on IMAP you can set it to only deliver mail from now on, or to deliver ALL mail to the IMAP client).
So, while this may not be a complete answer, it is the best that is possible given the details of the question.