In this scenario, an on-premise user was created and synced with Office 365. The Office 365 user has an Exchange Online mailbox, but this mailbox is not visible in the on-premise Exchange Admin Center.
While the Office 365 admin center GUIs are decent, there are many Office 365 management tasks that are better suited for PowerShell. However, before you can start scripting, you must first establish a connection to your Office 365 tenant.
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.