In a Microsoft Exchange Server 2019 or Exchange Server 2016 hybrid environment, you use Exchange admin center (EAC) to add users into a distribution group. Additionally, into the other tabs inherent in a distribution group. However, if the user that needs to be added is a remote shared mailbox, the mailbox is not even available in the picker to be added. The same works fine when executed from Exchange Management Shell (EMS).
To fix this issue, install one of the following updates:
For Exchange Server 2019, install the Cumulative Update 5 for Exchange Server 2019 or a later cumulative update for Exchange Server 2019.For Exchange Server 2016, install the Cumulative Update 16 for Exchange Server 2016 or a later cumulative update for Exchange Server 2016.