I definitely would not delete the posts. If it's not important for others to see those threads/posts, then you can always just move them somewhere else where only you can see them, in a private forum accessible only by yourself. If your former mod can't access her old account, and those posts aren't returned in any search results, she's not going to know if you deleted them or not. For that matter, she wouldn't know even if you left things as they are, unless someone else with access to the threads ratted you out. Anyway, if nothing else, this way you wouldn't have to worry about post counts being affected.
If you want to keep the threads available to others, then yeah, maybe just delete any of her personally identifying info. Not sure what software you're using, but you could probably just use your spam tools to mass delete/replace some of that. But unless her posts contain info like her real full name, places where she can be reached, other sites she moderates or websites or companies she owns or manages, etc., then there's probably, in reality, little information that someone could use to establish her real identity for some malicious purpose. I've found this to be the case with most of the people who make these kinds of demands, who seem to think that their little personal anecdotes make them stand out in some unique way.
If you want to keep the threads available to others, then yeah, maybe just delete any of her personally identifying info. Not sure what software you're using, but you could probably just use your spam tools to mass delete/replace some of that. But unless her posts contain info like her real full name, places where she can be reached, other sites she moderates or websites or companies she owns or manages, etc., then there's probably, in reality, little information that someone could use to establish her real identity for some malicious purpose. I've found this to be the case with most of the people who make these kinds of demands, who seem to think that their little personal anecdotes make them stand out in some unique way.