Adding users and mailboxes changes slightly when working in hybrid Exchange environments.While adding a user in ADUC and licensing the user in Office 365 is possible, the user's Exchange attributes will never be synced with the on-premise environment.
Converting a user mailbox to a shared mailbox in a hybrid Exchange environment can be frustrating. Fortunately, there is a PowerShell command available that makes the entire process much simpler.
We see this one a lot: a domain controller that either crashed or was uncleanly demoted, but never removed from the Active Directory forest. Since the original domain controller is gone, we'll need to manually remove it from Active Directory.
Filtering what objects are synced to Azure AD is a common request and there are many instances where filtering by OU just doesn't cut it. One option is to filter users by their UPN suffix so that only users with the public FQDN as their UPN suffix are synced to Azure AD.
Sometimes you need to replicate changes between your on-premise Active Directory and Azure, but don't want to wait for the next scheduled sync. In these cases, the ADSync PowerShell module provides a very easy way to force synchronization.