Andrew
It would be a new claim for PIP be aware that the criteria is fundamentally different from DLA, especially where it was for a child.
As he will be 16 he will be treated as an adult and you may have problems acting on his behalf. If he is not capable of managing his own affairs then you should consider becoming his DWP Appointee, see
www.gov.uk/become-appointee-for-someone-claiming-benefits Our PIP Claim guide is on the following link and explains the claim process and the criteria he will need to meet for an award.
www.benefitsandwork.co.uk/help-for-claimants/pip Gordon