How long until I get contacted

Hello a couple weeks ago my boyfriend got into an accident, really minor other person was not in the car but we had waited for them to return to let them know they had a couple scratches on their bumper and our car got more damaged in the incident. We called our insurance already and explained the situation but yet we have not heard anything yet from the other side. They have the same insurance as my boyfriend and it’s been about 4 weeks now and the other party had told us they did indeed contact their insurance so I’m just curious on when he will hear from them so we can already start paying whatever is needed and get the whole ordeal over with. His recent payment was due 2 days ago so I’m hoping at least next month he will have his updated monthly payments