The rules might have changed, but his Mum is still entitled to the Child Benefit for a certain period of time. This is in case the change of circumstances is only temporary or at least definitely not permanent. It used to be 8 weeks and then she is required to notify the change of circumstances. Of course, there's a presumption that during this time the money is being handed over, but I don't think this is compulsory again because the change might be temporary. Also, she might be able to notify the change of circumstances and still be the claimant as long as the money is being handed over, but a formal arrangement would be made (sorry, can't remember how it worked).
You definitely need advice on this before you make a decision. There's too many things to be considered, mainly because his Mum is still around. I am sure you can make it as informal or formal as you want, but you need the advice to avoid getting anyone in to trouble.