Message windows can be set to automatically close upon the completion of a reply or forwarding of a message.
1. Click on the “File” tab and select “Options.”
2. Select “Mail.”
3. Go to the “Replies and Forwards” section and add a checkmark next to "Close original message window when replying or forwarding.”
4. Click “OK.”
These instructions, along with illustrations, can also be found in SharePoint > Software Users Group > Shared Documents > Outlook-Office 365 > Auto-close a Message after Replying-Forwarding.