A customer had a requirement for an email in their Office-365-email-hosted organisation to be forwarded to an external email address. They didn't want a mailbox for the email address on their Office 365 subscription. This is what I found to do.
This was from the Microsoft Office 365 Community Forums (https://community.office365.com/en-us/f/158/t/6767)
1. Create an external contact with the information of the not yet created externally associated account you want the alias to go to.
2. Create a distribution group with the alias being what you want the internal address to be. I used the following settings. (NOTE: I think some of the settings were not available until I saved the initial group and then went back in to edit it)
a. Add the external account to the membership
b. Delete your own account from the membership
c. Under "membership approval" set both the "Closed"
d. Under "delivery management" set to "Senders inside and outside of my organization"