Hi @Wendell Jones ,
The possible cause is that after the mailbox move is complete, the Exchange Server 2016 continues to proxy the EWS request to Exchange Server 2010 .
Please refer to the resolution in the following link to restart the Autodiscover Application Pool and the Exchange Web Services Application Pool and see if it works.
Can't see Free/Busy info after a mailbox moves to Exchange 2013 or 2016 - Exchange | Microsoft Learn
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