Using a product called Crossware, we are able to automatically append signatures to e-mail messages at the transport level. Initially we were having issues with a Signature being applied to a group of users. We verified that the user was a member of the correct group, tested the user within the Crossware web application and all looked well. We then tested using Microsofts Graph API (https://graphexplorer.cloudapp.net) in order to verify that the user was a member of the appropriate groups. It's there we noticed that the user was not showing in Office 365 as part of any of the Distribution Groups that they should be a member of that were created for this signature application. However the Groups did show up in the Office 365 console. At this point I took to powershell and ran a Get-DistributionGroup command against our Office 365 Tenant. It was here that I noticed that the groups were not listed:
It was at this juncture I noticed while looking at the Distribution Groups in Active Directory, that they didn't have the mail or DisplayName attributes filled out. Turns out that when you create a Distribution Group on premise where you don't have an Exchange Environment, those attributes are not created automatically.
If you go and add the DisplayName attribute and assign it a mail address, the item will now sync with Exchange Online vs. Just office 365.