Help with stray cat vet bill

Hi, my name is Isabella. I was driving down Woodlawn Dr around midnight on 4/18 and passed by a kitty crawling to the side of the road in obvious distress. As an immense cat lover, I could not convince myself to keep driving. I approached the young cat and could tell she had been seriously injured and was refraining from using her back legs. I believe she was hit by a car. She looked so exhausted and wasn't defensive or aggressive at all, so I knew she was thankful someone stopped. I took her to an emergency vet and they were able to perform some x-rays and find a microchip. With the x-rays, it was found that the kitty has a broken pelvis and excess air in her lungs. They explained that the lung problems should resolve on their own, but her pelvis will need surgery. The microchip is addressed to Young Williams, however, they are not claiming responsibility for her. It was most likely a catch and release spay performed by them. Because of this, the emergency vet believes euthanasia is the most convenient option if no one takes responsibility. I can't even begin to believe to think about ending a kitty's life because it is inconvenient. I would like to claim responsibility for the time being in order to get the kitty the care she needs. The surgery is estimated at $6,000+. Beyond getting help with the surgery costs, I am also looking for someone to adopt her as I unfortunately don't have the capacity to care for her long-term. As of the afternoon of 4/18, she is still in the care of the emergency vet, but they are wanting me to pick her up tomorrow morning to care for her until they can perform surgery next week. Please help me cover the costs and help save this kitty. ****update-Young Williams is now claiming responsibility, as this cat was a part of their community cat program. However, I am still the person who discharged it and took it to Young Williams and was charged for the stay, medication, scans, x-rays etc. I am looking for help with this cost while I await for Young Williams to notify me if they can cover it or not, if so, all current donations will be refunded. Thank you all for your concern, it means so much. Hopefully the Kitty will be available for adoption through Young Williams shortly.