Step 1: open outlook and go to file >> Accounts settings (on outlook 2013), for older versions, go to tools >> account settings

Step2: Double click on the account you want to change

Step 3: Click on the “More Settings” button

Step 4: Tick the option “Leave a copy of messages on the server” AND tick “Remove from the server after….”. Messages will only be removed X days after they have been downloaded for the first time.
If you also download mail from another device, 14 days should give you plainty of time to also download them on the other device.