DistroList Group Delegation is an important 0365 feature in order to avoid someone sending as a distro list even if that person is not authorized to do so.
To allow a user to send masked as a distribution list, search for the distribution list in 0365 Admin-Exchange. To know more about 0365 distribution lists, read this.
Open the distro list’s propertied and go to group delegation section. Add the user in send as. Click the save button for changes to take effect.

Note: A user that will be allowed to send as the Distro List should have a mailbox or contact entry in 0365.