The idea behind Outlook is that it will download your E-Mails from the server. Each time you use it the mail is transfered from the server to which ever PC you are using Outlook on at the time.
I have never tried it but you could use the 'leave copy on server' facility.
Run up Outlook and go to the Menu Bar.
Select Tools & Accounts.
Once you have your mail accounts on display highlight the one you want to change and press the properties button.
Go to the Advanced tab and down at the bottom you should see the option 'Leave a copy on the server' - put a tick in and press OK.
I don't know if this will work but it's worth trying.