He didn't. Jack the Ripper was never caught.
No
Jack the Ripper sent a letter to the police saying at the end "Yours truly JACK THE RIPPER" ever since then it has been his alias
Police did not possess the tools needed to catch this type of killer. The science was just not there. It had nothing to do with conspiracies involving the royal family or Scotland Yard cover ups, the Ripper case needed modern forensics.
Jack the Ripper was never found.
Catching criminals was the job of Scotland Yard's police force. When the Ripper proved uncatchable of course police were criticized for 'letting him get away.' Most people don't know that the police tried very hard in their pursuit of the Ripper. They just did not possess the knowledge and tools needed to catch the type of killer the Ripper was. Chances are very good that Jack would have been apprehended had the police had modern crime solving techniques.
Some Ripperologists believe that the police actually did capture Jack the Ripper. Some say the police were to blame for not cathing him. The reports of Jack the Ripper were collected and reported by the police, but then the different newspapers with their political influences slightly distorted the stories to give them their own effect.
Jack the ripper was the first serial killer to reach the media. The world has eyes on him. It was a scandal about the condition the police was at that time. There were no false starts in this case. There was nothing to go on but the remains of the victims. Even today it takes quite some time to catch a murderer on the run, but in the case of Jack the Ripper, there were many aspects police today would not come across.
Police found no evidence on Jack The Ripper pertaining to Mary Kelly or any of the other victims either. Jack was never caught.
Scotland Yard never claimed to have captured Jack The Ripper and in fact were ridculed for their inablity to catch him. It resulted in many conspiracy theories, some involving the royal family, the police force and even Inspector Fredrick Abberline.
He killed and ripped woman's bodies. The police received a boasting letter from a man claiming to be the killer. It was signed Jack The Ripper.
The serial killer from London's Whitechapel district in the late 19th century gave himself this name in letters sent to the Metropolitan Police at Scotland Yard, and to the local press. It is not uncommon for serial killers to correspond with police in a risky game of cat and mouse. The goal, to prove he is smarter that those who are trying to catch him, namely, the police.