Many years ago my when my DD was about 12 she kept getting nits, as fast as I got rid of them she got them again. Then one day when she was at my house I noticed her best friend was absolutely riddled with them, I asked her if she wanted me to go through her head with my 'special comb' (nitty gritty had just been invented) for literally hours she sat there and let me go through her head, when we were done she gave me a hug and cried, I asked her why she was crying, she replied she has her mum, dad, sisters etc and I was the first person to ever care enough about her to go through her hair for her. She knew she had them, she'd tried to get them out herself and had asked for help but got none.
I took her home and told her mum what I had done, thankfully I didn't get slated for overstepping but if I had I'd have let rip, kids gets nits, it happens, kids being riddled constantly imo is neglect
I hope your bfs little one isn't going to be crying in someone else's lounge in years to come.
Please don't give up on her, keep on at him, speak to the school, health visitor, or social services, maybe now someone else has spoken to him he might let you show him how to comb her hair, Thank you for caring about her 💐