Dubious business ethics

We run a guesthouse and received a 3 night booking for a guest from Prospur Travel. We confirmed the booking by email. Our terms and conditions and cancellation policy is stipulated on our booking confirmation form. We were then requested to send an invoice for the accommodation. This implies that our cancellation policy is accepted. We waited until around 01:00 for the guest to arrive. He did not show up. I phoned Prospur Travel the next morning to inform them of the non-arrival. It then became clear the Prospur Travel booked the guest into another guest house without informing us or cancelling the booking! Our cancellation policy stipulates that we are entitled to the full amount for the accommodation in the event of a no-show. I spoke to the office manager and explained that we will be charging the cancellation fee. We decided to charge 50% of the full amount and sent Prospur Travel the invoice for that amount. Since then we have made numerous calls in an attempt to follow up on the invoice. The fact the booking was confirmed meant that we could not accommodate other guests in that room meant that we had loss of income. Do the right and pay your invoice!