Yeah, one thousand percent this.
Also, she WILL find out. I hate the narrative that says “girls are mental” cause we aren’t, not at all, but humans in general are perceptive and if she doesn’t sniff out that something is amiss via her intuition then her friends will one million percent find it out via social media stalking etc.
Really nastily unfair to ask prof to lie as well cause when it does get found out, which it will, the girl and all her friends will hate him and think he’s a deceitful bastard too