Should my sister sue her ex-boyfriend for badmouthing her to other people?

They broke up over 11 years ago, and he's still hung up over this high school relationship! To this day, he badmouths her whenever I am around him or he's around her friends. Not only that, he tries to spread nasty rumors about her. ("She sleeps around, has a ual disease") Its clear from my standpoint that he will never stop. I told my sister that she should sue the guy for harrment at the least. Her lawyer told me there's a workaround to sue him for slander even though all the things he said had no effect on her (she has a good job, good income, and happily married now). I am waiting for the next time he badmouths her in a large setting, thats when I feel she should make her move to sue him. In my view, I told her its worth doing so regardless if she wins or loses because this can finally be legally doented and put on his (already) growing police record. And maybe this will finally be the incentive for him to move on. I would like to know what you think on this matter.