Should I tell my SIL that my husband’s brother has cheated on her?

My husband’s brother (38yo) is dating a woman (49yo) for more that 2 years.
Due to unrelated circumstances we no longer have any relationship with my husband’s family. However, I found out that he repeatedly cheated on his girlfriend with a coworker and that makes me very angry.

I have considered sending her an anonymous message to tell her about it, but there is something that worries me: they each have a child from previous relationships, and they have built a family life together. I feel bad for the kids, but at the same time it’s unfair to her. He is the typical narcissistic person and she is a people pleaser, it wouldn’t surprise me if she ended up forgiving him.

On the other hand, I am not sure how my husband would feel if he found out what I had done.
Should I send her an anonymous message without anyone knowing, or should I stay silent?

Sorry if there is any grammar mistake, english is not my first language.

Thanks in advance for any advice!