This article applies to:
Office 365 users don’t see on-premise dynamic distribution lists in their Outlook Address Book.
Due to architectural differences in local Active Directory/Exchange and Office 365, the on-premise Dynamic Distribution Groups do not get replicated to Office 365. This is by design.
In Office 365 Exchange online administrative console create mail enabled contact that points to the dynamic distribution list in the on-premise environment.
To create a contact in Exchange Online to represent the dynamic distribution group, follow these steps:
1) Login to Exchange Online admin console.
2) Under Recipients/Contacts click on the Plus sign and select Mail Contact
Fill out the details. In the external e-mail address field enter the e-mail address of your on-premise dynamic distribution group. The change will be visible to clients after the next Offline Address Book rebuild (takes place once in 24 hours).
Once you have moved all your on-premise users you can remove this temporary solution and create equivalent Dynamic Distribution Groups in Exchange Online.