Forgive my skepticism but this doesn't pass the smell test. In order to transplant the new spinal cord, they must first remove the old one. This involves cutting through the spinal bones and discs, then cutting the existing spinal cord out and severing all of its nerve connections to the rest of the body.
The reason spinal cord injuries are so problematic is because the spinal cord nerves do not heal when cut. (The only exception being the lower lumbar portion.) I'm failing to see how severing the old cord to replace it with a new one won't just result in a more seriously paralyzed patient.