Harold Frederick Shipman (14 January 1946 - 13 January 2004) was a British general practitioner and one of the most prolific serial killers in recorded history. On 31 January 2000, a jury found Shipman guilty of fifteen murders for killing patients under his care. He was sentenced to life imprisonment with the recommendation that he never be released. The Shipman Inquiry, a two-year-long investigation of all deaths certified by Shipman, which was chaired by Dame Janet Smith, examined Shipman's crimes.

In March 1998, Linda Reynolds of the Donneybrook Surgery in Hyde, prompted by Deborah Massey from Frank Massey and Son's funeral parlour, expressed concerns to John Pollard, the coroner for the South Manchester District, about the high death rate among Shipman's patients. In particular, she was concerned about the large number of cremation forms for elderly women that he had needed countersigned. The matter was brought to the attention of the police, who were unable to find sufficient evidence to bring charges; the Shipman Inquiry later blamed the police for assigning inexperienced officers to the case. Between 17 April 1998, when the police abandoned the investigation, and Shipman's eventual arrest, he killed three more people. His last victim was Kathleen Grundy, who was found dead at her home on 24 June 1998. Shipman was the last person to see her alive and later signed her death certificate, recording "old age" as the cause of death.  In August 1998, taxi driver John Shaw, from Hyde, contacted the police, informing them that he suspected Shipman of murdering 21 of his patients. Grundy's daughter, lawyer Angela Woodruff, became concerned when solicitor Brian Burgess informed her that a will had been made, apparently by her mother. There were doubts about its authenticity. The will excluded her and her children, but left PS386,000 to Shipman. Burgess told Woodruff to report it, and she went to the police, who began an investigation. Grundy's body was exhumed and when examined, was found to contain traces of diamorphine, often used for pain control in terminal cancer patients. Shipman claimed that she was an addict and showed them comments in his computerised medical journal, but a program on his computer showed they were written after her death. Shipman was arrested on 7 September 1998, and was found to own a typewriter of the kind used to make the forged will.  The police then investigated other deaths Shipman had certified, and created a list of 15 specimen cases to investigate. They discovered a pattern of his administering lethal doses of diamorphine, signing patients' death certificates, and then falsifying medical records to indicate that they had been in poor health.  Prescription For Murder, a 2000 book by journalists Brian Whittle and Jean Ritchie, advanced two theories on Shipman's motive for forging the will: that he wanted to be caught because his life was out of control, or that he planned to retire at age 55 and leave the UK.  In 2003, David Spiegelhalter et al. suggested that "statistical monitoring could have led to an alarm being raised at the end of 1996, when there were 67 excess deaths in females aged over 65 years, compared with 119 by 1998."

Using a quote from the above article, answer the following question: How did he kill them?
the last person to see her alive and later signed her death certificate, recording "old age" as the cause of death.