Ahem,
In that same options view you may specify one(I recommend one) to remove after being left on the server after XX number of days.
Or, you can specify one to remove of server when it has been deleted off that systems deleted items folder as well.
Personally, I would tell you to use one system, and access from the other locations with aweb mail proram, the good ones will let you send rcve, but do not remove off the server.