My boyfriend just got his divorce finalized and also got full custody of his daughters but now his ex is sending him harassing texts and filing false cases with child services, what should he do?

Here is a very useful article
Falsely Accused? - How to Deal with Child Protection Services - Yahoo! Voices - voices.yahoo.com (http://voices.yahoo.com/falsely-accused-deal-child-protection-630799.html)
... and my point of view about RO
https://www.askmehelpdesk.com/family-law/restraining-orders-499600.html

I suggest your boyfriend get a lawyer. I am not a lawyer, nor a professional in this area. I did get divorced after my first 7 yrs of marriage, and had a lawyer. If his ex-wife is going to all this trouble to be a pain, then he needs someone to tell him legally what he can and can't do. Best of luck.