Child maintenance service arrears

My step son 18 has lived with us for 5 years with little contact with mum. She refused to pay cms so it is now taken from her wages, when she works.

When he finished college in May he is going to move in with her for a few months so he can put her down as the parent supporting him so he gets more money when he goes to uni.

When we contact cms to say he has moved in with her will they continue to collect the arrears?

I think it’s about 4K