Hi,
I have a few suggestions for your description.
- Check the connector, in the EAC, navigate to "Mail Flow" -> "Connectors". Make sure you have a send connector specifically for sending email from Exchange on-premises to Office 365.
- Check that the MX record is pointing to Office 365.
- After running the HCW, update the Receive Connector on the Edge Transport server to ensure it will accept mail from EOP securely.
We hope you can provide more information so that we can better solve your problem.