Question
What is correct way to create shared mailbox in hybrid environment.
Answer
From the Exchange on-premise interface, we can create “remote mailbox” for users, Resources or Rooms. You should create the mailbox on-premise so that the object exists in Active Directory (AD) and it contains the Exchange attributes which is manageable via the on-premise Exchange admin center (EAC).
Create a normal mailbox (or Room) with the Exchange On-Premises admin interface, then convert this mailbox in a second step as shared with the Exchange On-line interface.
new-remotemailbox with the option -shared or enable-remotemailbox to create in one step the correct object (from Exchange on-premises admin shell). This will provision the shared mailbox directly in Exchange Online which will prevent you having to move it.