The easiest way to create a synchronized shared mailbox is by using Easy365Manager to create it after the AD user has been created but before the user is synchronized to Office 365 (read this for more details).
If the user account has been synchronized to Office 365, you need to use a different approach:
- Temporarily assign an Exchange Online license to the user to create a mailbox.
- This can be done from the Office 365 tab in user properties.
- Change the mailbox type to Shared mailbox.
- This can be done from the Mailbox tab in user properties (once the mailbox has been created).
- Remove the Exchange Online license again.