I agree with this! I would reach out and say something like that - “hey, I just wanted to reach out and let you know that when I was at an age similar to your daughter, I had a negative / inappropriate experience with Nasty Trainer. I would like to keep this private, but I would be happy to discuss in more detail should you wish.”
The you’ve warned them and they can get more detail in person. I wouldn’t want to send the screenshots in case they were sent on.
I don’t think there is a “legal” duty via SS since they have already seen this evidence, but I believe there is a moral obligation. My parents did not send me to a trainer as a working student due to something said to them - I am very glad I was not subjected to anything as a result.