One of the fairly common tasks for Exchange administrators is to configure forwarding on a mailbox. Previous versions of Exchange gave you the option to leave a copy of forwarded messages in the mailbox and the option was accessible in the graphical administration tools. As you can see in the screenshot below, for some reason in Exchange 2013 this option was left out of the graphical/web interface.
When you enable forwarding in the web interface, by default the message will not be left in the recipient mailbox. However, the option is still there if you use PowerShell.