These steps will let you use your AD-synchronized distribution groups and also send email to Shared Mailboxes that exist purely in Office 365.
- Create a Contact object in your active directory. Set the email address to a unique value, fill out the Display Name property and other contact properties as required. Since this contact will be used to represent the Shared Mailbox, name it to help you identify it as such.
- Modify the targetAddress attribute on the newly created Contact object and set it to the email address of your Shared Mailbox. If you do not see the Attributes tab on your contact object, close the object, and make sure that Advanced is checked in the View menu of your Active Directory Users and Computers console.
- Add the new Contact to your AD Distribution group.
- Wait a few minutes to make sure changes propagate through your AD infrastructure
- Initiate directory synchronization, or wait for dirsync to take place on its normal schedule.
Once you complete the above steps, mail sent to the distribution list will also be delivered to the Shared Mailbox.