>If your iPhone has been set up to access that account as an Exchange mailbox (i.e. Exchange ActiveSync), it should sync automatically - when you delete an Inbox message in Outlook, it also gets deleted from your iPhone. There may be some short delay but it should be pretty quick.
Yes, that part works. What I don't want is all the Inbox messages already read in Outlook. We had that support before. Exchange does not support that. This is where the problem is.