Help?How can he gain custody?

My boyfriend and I have been together for a long time now and ever since I've known his 6 year old son and 3 year old daughter, he has been the custodial parent. Six months ago his ex who left him and his kids so she could live a life of partying showed up back into their lives begging him to let her see the kids. Keep in mind also that she is with another man and recently has had another child with the new guy in her life. My boyfriend decided it would be ok to allow the kids to stay over with her every other weekend. Things were going ok until she had her nerve to serve him joint custody papers. My boyfriend has written statement from her when she lefted them and papers she has signed declaring that he had full custody (even though no custody has been established). Does she have a good chance in winning custody?She petitioned that she wants joint custody because his son is not doing well in school and she does not want my boyfriend to try to move anywhere else within the state. Please any advice will be helpful thank you.