Updated Dec 8th 2011 to remove reference to LegacyExchangeDN
In Office 365 with Hybrid Deployment, if you create Dynamic Distribution Groups on the on-premises Exchange organization, these objects are not replicated to Office 365 via DirSync. Therefore for mailboxes in the Office 365 cloud they will not see the Dynamic Distribution Group in their Global Address List, and so therefore can only email the members of the list by sending an email directly to their email address.
To show the Dynamic Distribution Group in the GAL in the cloud, you need to add a MailContact to the cloud that represents the Dynamic Distribution Group. This MailContact object should have the following mappings:
|On-Premises DDL||Cloud MailContact|
Note that this MailContact object is made in Office 365 or Exchange Online and not in the on-premises AD. It is not replicated to the cloud via DirSync. If it exists on premises then the name for the DDL will appear twice in the on-premise GAL, once as a DDL and once as a contact object.
To determine the information need for the cloud contact object, run the following in Exchange Management Shell on premises:
Get-DynamicDistributionGroup | fl Name,EmailAddresses,LegacyExchangeDN
An alternative is to create the DDL in both the cloud and on-premises, but this can only happen if the attributes you are filtering on on-premises are replicated to the cloud via DirSync.