This picture of Mr Lace was taken when he was about 15 years old
Police have named the man they say was "responsible" for the murder and rape of a woman in 1979.
Detectives have revealed the DNA of David Lace, 26, whose remains were exhumed last month, matched that of the suspected killer of Teresa De Simone.
The 22-year-old victim was found in her car at the pub in Southampton where she worked part-time, in December 1979.
Sean Hodgson, 58, of County Durham, spent 27 years in jail for the murder before his conviction was quashed.
Mr Lace, whose natural parents are both dead, was originally from Portsmouth and, at the time of the murder, he was 17 and living in the city.
He was born with the surname Williams, later taking the adopted name Lace.
Detective Chief Inspector Phil McTavish describes David Lace's convictions
He took his own life in December 1988 when he was living in Brixham, Devon. He did not feature in the original police investigation and was not thought to have had prior links to Miss De Simone.
He made admissions to the murder in 1983 following Mr Hodgson's conviction at Winchester Crown Court some 18 months earlier.
In a statement his family said: "We have been left shocked and saddened at the latest news that David has been shown to have been responsible for such a terrible crime.
"We very much wish to extend our sympathies and condolences to Teresa De Simone's family at what must be a very difficult time for them."
The Ministry of Justice gave permission for Mr Lace's body to be exhumed from Kingston Cemetery, Portsmouth, after new DNA samples taken from his siblings indicated he was the prime suspect in the case.
Teresa De Simone's mother said she was a "happy girl, but shy"
Det Ch Insp Philip McTavish, of Hampshire police, said: "We are satisfied we have identified the man responsible for the murder and rape of Teresa De Simone and we are not seeking any other person.
"We are not linking David Lace to any other undetected serious crimes."
Hampshire police have voluntarily referred the matter to the Independent Police Complaints Commission.
Det Ch Insp McTavish said officers looked into Mr Lace's confession at the time and decided it revealed "numerous and significant inconsistencies".
They included an incorrect description of the car's colour and number of doors, incorrect timings and incorrect descriptions of Miss De Simone's clothing and watch.
His description of the violence used was also inconsistent with the victim's injuries.
The handbag Lace had concealed was never found, Det Ch Insp McTavish added.
He said seven men, including Mr Lace and Mr Hodgson, had confessed to the crime but added that very limited and original paperwork was available.
"We are not aware of the full content of these confessions or indeed the full rationale for the exclusion of these men from further consideration," he said.
The Crown Prosecution Service (CPS) confirmed it would have enough evidence to charge Mr Lace if he was still alive.
Alastair Nisbet, senior crown prosecutor for Hampshire & Isle of Wight, said: "But this is in no sense a declaration that he was guilty of the offences.
Mary Sedotti said the past six months had been difficult
"Had Mr Lace lived, our decision would merely have authorised the police to begin the legal process by charging him."
Miss De Simone's partially-clothed body was found in the back seat of her Ford Escort in a car park beneath the Tom Tackle pub, where she worked behind the bar part-time. Her main job was as a clerk for the gas board.
Her mother Mary Sedotti, 77, said the naming of the suspect would give some closure on the matter.
"It is a relief to get it all done," she said. "Hopefully, we can all start to move on now.
"In a way it's hard knowing that he is not here to answer or explain. But then, at the same time, I think that what he did shows he must have had a conscience."
Mr Hodgson confessed at the time of the original inquiry to killing Miss De Simone.
But he pleaded not guilty at his 1982 trial at Winchester Crown Court, where his defence team said he was a pathological liar.
After Mr Hodgson's conviction was quashed at the Court of Appeal in March this year, police carried out DNA screening of more than 100 people.
Hampshire police said it was one of the rare times the suspect in a historic murder inquiry had been exhumed in the UK.
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