Notify a task owner when the parent case has a new conversation update

Notify a task owner when the parent case has a new conversation update

Hello, I have been trying to find a good way to update task owners if the parent case has an update in the conversation tab. We use Service request for when HR notifies us for a new hire. If HR updates the case, say the start date is now different. can the task owners be notified of the new comment? 

Thanks. 

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