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Martin Stewart had been freed eight months into a two-year sentence for robbing another elderly woman when he targeted the home of Margaret Grant on January 24 2020.
Just 48 hours after leaving prison, he ransacked the flat and stole cash - including £200 from a charity box - before shoving the 79 year-old to the floor when she tried to get help.
Stewart, 41, only fled when Margaret's carer turned up at her home in Restalrig Circus in Edinburgh.
The OAP suffered a heart attack as a result of her ordeal and tragically died in hospital.
Stewart was later caught - but only after he had stolen from a number of other pensioners in the capital.
He pled guilty to the culpable homicide of Margaret during a hearing at the High Court in Glasgow. Stewart had originally faced a murder charge and was remanded in custody to be sentenced next month.
The court heard Stewart had 18 previous convictions mainly for "bogus workman" crimes preying on the elderly in the homes.
His last offence was in March 2019 when he was sentenced to two years for the assault and robbery of an old woman.
But, he was released eight months into that term - just two days before he went on to kill Margaret.
Prosecutor Greg Farrell said Margaret lived alone and needed carers three times a week.
Despite being almost housebound, the pensioner was described as reasonably well as well as a "popular and much loved member" of the local church community.
Stewart turned up at Margaret's ground floor flat around 6pm on the night of the killing.
Mr Farrell: "He induced her to let him in by pretending to be a postman with a parcel for her.
"Once inside, he grabbed Margaret by her dressing gown and demanded money.
"She told him she only had £15 in her glasses case. He called her a liar and then searched the flat."
He pocketed the £15 as well as the £200 Margaret kept in a charity tin.
Stewart also rifled through Margaret's handbag as she then told him she was going to get help.
But, the killer grabbed her again and threw the four-foot pensioner to the ground.
The OAP's carer came to her rescue and Stewart ran off - but his DNA was left at the scene as well as his fingerprints on a Christmas card.
Margaret - who already had a number of medical issues - was taken to hospital.
She was initially able to talk freely, but her condition got worse and she passed away that night in hospital.
A medical consultant concluded the pensioner had suffered a "major heart attack" as a result of "acute and severe stress" from what happened.
Stewart remained at large and targeted five other Edinburgh properties between January 27 and February 17.
He had also tried to steal an 89-year-old woman's handbag on the day he was freed from prison.
Stewart claimed to the other elderly victims that he was a workman - including lying to one he was there to fix a flood in the area.
He was finally arrested on February 18 at a flat in the capital's Willowbrae area.
Ian Duguid QC, defending, said: "He is deeply sorry and ashamed for all this offending.”
Prosecutors have moved for a risk assessment to be carried out on Stewart, which could see him served with an Order for Lifelong Restriction.
Lady Stacey adjourned the case until next month.