Abbey Cape, from Ashby-de-la-Zouch in Leicestershire had the operation at Great Ormond Street Hospital in London.
She'd been on a life-support machine since 13 April.
Plea for donors
A donor was finally found and Abbey had the transplant a few days ago.
Abbey's school pals have rallied around her, and have made tapes of themselves singing and telling stories, to play to her in hospital.