The operation took place at Great Ormond Street
A baby girl remains seriously ill after her conjoined twin died following emergency surgery to separate them.
Hope Williams died on Tuesday night after an operation at London's Great Ormond Street Hospital.
Laura Williams, 18, from Shrewsbury, gave birth to her and sister Faith at another London hospital on 26 November.
Surgeons said Faith was "very sick" and had a 50-50 chance of survival. She was still in a stable condition in intensive care on Thursday.
In a statement, Great Ormond Street Hospital said: "Faith Williams is a very sick little girl.
"Great Ormond Street Hospital is doing everything it can for her, and we continue to offer her the highest possible levels of care."
Professor Agostino Pierro, head of the surgical team, said Hope's lungs proved too small to support her breathing after the separation.
The twins were delivered by Caesarean section at London's University College Hospital last Wednesday with a combined weight of 4.8kg (10.5lb).
They were later transferred to Great Ormond Street.
The sisters were joined from the breastbone to the top of the navel and had a shared liver but separate hearts.
Mrs Williams and her husband Aled, 28, from Anglesey, were with Hope when she died.
The hospital had wanted to wait until the twins were stronger before carrying out the operation, but it was brought forward after their health gave cause for concern.
Mrs Williams is believed to be the youngest mother of conjoined twins in Britain.
The condition, which is extremely rare, occurs when the single egg from which identical twins develop fails to divide properly after conception.
Medical staff warned Mrs Williams and her husband that their babies might not survive after a 12-week scan revealed the problem but they refused to consider a termination.