Login to Admin and Select Exchange, then MailFlow. Select Connectors and then select the + to add a new connector.
Choose Office 365 in the From category and choose Partner organization in the To category
You will be prompted to name the new connector. The choice is a personal preference but something like MailRoute Outbound would be optimal for future reference.
Click Next and your next screen will prompt you when do you want to use this connector. Select "Only when I have a transport rule set up that redirects messages to this connector"
You will prompted to choose how to route email message. Select "Route email through these smart hosts". Click on the + and add "outbound.mailroute.net". Click Next.
Your next screen is a confirmation of your selections. If everything looks correct, click Next.
You may validate your new connector to make sure it works.