To do that via Outlook I believe you'd need to add the rule to the shared mailbox itself, eg not within your own mailbox, so you'd need to login direct to that shared mailbox in Outlook, or login to it via Outlook Web Access and then create the rule in there.
That said, if the rule and the script it runs handles the contents of the message I have a suspicion that it will be flagged as an "on this machine only" rule, in which case you won't be able to get it to run without Outlook on that specific
machine running, so I'd check first of all how it's recognised in Outlook in your own account. There are various things which can cause the rule to only work on a specific machine (or to only run when Outlook is running), which you can see here
http://www.msoutlook.info/question/371