One of my clients' preferred way to handle a departed employee is to set up an autoreply and forward the email to another staff member. This doesn't work as it should on Office 365. With a regular on-premise Exchange server, you can set up the autoreply in the mailbox and configure forwarding with still delivering the message to the departed user's mailbox, and it works as intended.
With Office 365, the forwading happens, but the autoreply doesn't go out even though the mailbox is configured to receive the message. Very annoying.
To get around this, I had to configure the autoreply and set up an Outlook rule to forward the messages.
While researching this, I found this semi-helpful page on dealing with terminated employees when you have Office 365: