In Outlook, if you try to set up a a rule to "Forward" mails to e2t2, it won't work because it will forward them differently. It doesn't send an exact copy of the original email. To make e2t work, you need to set up a rule to do what Outlook calls a "Redirect" instead. Here is an article explaining Forward vs Redirect in Outlook.
Additionally, here's how to set up a redirect rule in Outlook, with screenshots.
There's a couple more complications - according to this page, "Redirection requires you to use a Microsoft Exchange Server account." In a regular old Outlook account, you won't find the option to redirect, so you won't be able to set up e2t properly.
Furthermore, not all exchange servers can support redirect.