CLAIMING VAT ON PAYMENT OF THIRD-PARTY LEGAL COSTS

My client has been in dispute regarding a road traffic accident between one of his company’s lorries, and another VAT registered business’ lorry. A small claims court has judged in favour of the third-party business, and has awarded them payment for damages, including reimbursement of their legal costs. The third-party is a partially exempt business, and so they would like reimbursement for the net amount of their costs, plus the VAT – will the third party raise a VAT invoice to us for payment of those costs and can my client claim back any of the VAT?