Hi @Ramki
What is the coexistence mode for the SFB hybrid with Teams?
Is this picture is your problem in your organization?
Based on my experience, Messages sent to TeamsOnly users will always route to Teams. Messages sent to Skype for Business users will always route to Skype for Business. Messages sent to Islands users will always route to the same client from which they were sent. So please try to change the partner coexistence mode to Teams only and see if it can be worked.
In addition, please check both organizations should be enable federation. For hybrid environment federation, you could refer to this table's steps to check it.
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