Possible to file for custody?

My boyfriend and his ex split over 4 years ago…they have an 8yo daughter. There’s no custody agreement but he pays child support. Until he got a promotion he was working 2 full time jobs and couldn’t take care of her, now he’s working one and making a better income. His ex lives with her parents and refuses to work. He wants to file for custody of his daughter because he has a steady home and income and his ex refuses to tell him anything that goes on with his daughter and tells the child not to tell him anything as well. His ex also has anger and instability issues and has been put under 72 hour psych evaluations on a few occasions, she also refuses to take her medications or get help for her drinking problem. Does my boyfriend have a good chance of being able to file? Can he file? Would it work in his ex,s favor that she lives with her parents?

He can definitely file, but he’d have to make a really strong case to receive sole custody.