If she is the one who has legal custody of the child, how much he stays with her isn't really an issue that the people who certify for food stamps are going to come after, unless it is questioned, he's considered a member of her household, and she probably has the papers to prove it. By the way, how do you know she's been claiming him and receiving assistance for him for the last 3 years? As someone has said, usually when a mother applies for assistance listing children, great interest is paid in who is the child's father and is there any way some support could be obtained from him.
And if it is investigated, and she maintains the child was with her, was a member of her household for SNAP purposes at least most of the time during the last three years, with her having custody, it's like your word against hers that he's lived with you the whole time and there's probably not going to be any fraud determined. If there is a fraud determination, it might get her sanctioned, barred from getting SNAP for a while, but as I continuously belabor the point, if they criminally prosecuted every public assistance case they run up on, they'd have no jail space for any other kind of criminal behavior and or time to try the cases. It will not be something that you'd need to bring up while seeking custody. If you are awarded custody, you can make sure she doesn't do it anymore.