Please check if the affected profile has read access to both Contact and Lead Objects, in the event that nothing happens when a user clicks on the reply, reply all, and forward links. Enhanced email requires that read access be provided on the email field for both Contact and Lead. Also note that these links only work if the user has access to both Contact and Lead objects.
To check a Profile:
Additional Resource:
Reply, Reply All and Forward emails in Lightning Experience
000383507

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