Yes, it is possible to leave copies of the e-mails in the mail server with Outlook Express. Please refer to the following for the procedure.
1) Start "Outlook Express".
2) Click [Accounts] from the [Tools] menu.
3) Click the [Mail] tab, select your account and then click the [Properties] button.
4) Select the [Leave a copy of messages on server] check box in the [Delivery] column of the [Advanced] tab and click [OK].