If you created a distribution group in Office365 and it was sent to external people for their use, they will likely initially get the following error:
The group xyz only accepts messages from people in its organization or on its allowed senders list, and your email address isn't on the list.
Note enabling external users to send email to the list is controlled in two places in Office365 and the both must be enabled. The first location is located in the general “Edit” the properties of the distribution list itself.
The other Location is in the Exchange properties…and is accessed from the Distribution List Properties > Edit Exchange Properties.
Once in the Exchange properties to to > Delivery Management and select the option: “Senders inside and outside of my organization”