In Lead settings, turn ON "Relate Emails to Contacts Upon Lead Conversion" in advance. With this enabled, when a Lead is converted to a Contact, emails that were sent during the Lead stage are automatically associated as if they had been sent from the Contact — so the "Reply" action after conversion works without error.
If the setting above was left OFF and the conversion has already happened, instead of clicking "Reply" on the affected email on the Contact record, send a new email from the Contact record using the new Email action. Once this new email exists as the starting point, subsequent "Reply" actions on end-user responses will work without error.
Reference: Define Default Settings for Lead Creation
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