Simplest way is just to set both Outlook clients to access the same mailbox via POP3, and set them both to "keep messages on server, delete after 7 days" (options are in Tools, E-mail accounts, View or change e-mail accounts, select the account, hit change, hit "More Settings", select the "Advanced" tab. Personally, I have three computers (work, parent's computer, parent-in-law's computer) all set up to "keep messages on server", with no expiry time, and my main home computer set to delete them after 7 days.