Hi @SY_MSO ,
Check the mailbox in the EAC of on-premises Exchange. Is the displayed mailbox type Office 365?
1.Agree with what Andy said. First, please check whether the RemoteRoutingAddress you have set is correct, usually the format is "user@tenant .mail.onmicrosoft.com".
2.Please open Active Directory Users and Computers in DC, and check "Advanced Features" in "View". Then find the AD account associated with the remote mailbox. Check the value of "MSExchMailboxGuid" in the attribute, which is empty by default. If it is not empty, please try to clear the "MSExchMailboxGuid" and "targetAddress" attributes, and run the following command line to force AAD connect to synchronize, and then check whether the remote mailbox appears under "Mailboxes".
Start-ADSyncSyncCycle
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