Exchange hybrid writeback
A hybrid deployment offers organizations the ability to extend the feature-rich experience and administrative control they have with their existing on-premises Microsoft Exchange organization to the cloud. A hybrid deployment provides the seamless look and feel of a single Exchange organization between an on-premises Exchange organization and Exchange Online.
To accomplish this scenario and allow your on-premises users to take full advantage of Exchange online, attributes from the cloud, must be written back to your on-premises users. Both cloud sync or connect sync can write back the attributes.
You can enable this scenario using cloud sync by ensuring you're using the latest provisioning agent and following the documentation. For more information, see Exchange hybrid writeback with cloud sync
You can enable the connect sync scenario through the installer. By selecting custom install, you can choose Exchange hybrid writeback. For more information, see custom install for connect sync