Right now updates to admin responses aren't tracked in the history of the Idea, so there is no way to know which aha user wrote and posted the admin response.
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Update: Thanks for the response! That's a great workaround option for us.
Thank you for the feedback!
We will look at adding the admin responses into the idea history. Until then, note that you can see the history of the admin response inside of the response editor itself. Click in the response, then select the clock icon at the top right of the edit toolbar.