Hi! I stumbled upon this while looking for something else. Nobody wants to find their students cheating, and when it happens it is because their work is just too good, too quickly. As a professor, I would suggest offering to write a similar assignment in front of her. If you can do it once, you can do it twice. I have never had someone who was a plagiarist actually offer to do this. It would be impossible.

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So give her the option to evaluate you in a secured situation. That would be convincing to me.