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Mary Donnelly, 38, was found dead in her Ebdentown St flat by her sister on August 30, 2012.
Former neighbour Kharn Tamaka, 29, was sentenced by Justice Ronald Young in the High Court at Wellington today to life imprisonment with a minimum non-parole period of 12 years.
Tamaka earlier pleaded guilty to murder.
Ms Donnelly had lived independently with family support and weekly check-ups from a caregiver. She was last seen with Tamaka at her flat the day before her body was found.
A victim impact statement from cousin Helen Moore - read aloud in court by Crown prosecutor Emma Light - said the family was reeling in disbelief that someone with special needs would be killed in such a brutal manner.
The "evil" murder would haunt them forever, and no words could explain the "sheer, cold horror" the family had been through.
In her statement, sister Donna Donnelly said the murder had destroyed the family. Their elderly mother, aged in her 70s, could no longer talk about Mary.
Ms Donnelly was described as soft and gentle in nature with a friendly, fun-loving personality.
She had a speech impediment, but that did not stop her pursuing her biggest passion of singing at a local karaoke club. She also painted and had won a local award for her art.
Justice Young said Tamaka had offered no explanation for the murder.
"It is no exaggeration to say that this was a shocking murder. It is hard to understand why you killed this young woman."
He said Tamaka had lived next to Ms Donnelly in 2011 and the two had known each other.
On the day before her body was found, CCTV footage showed him following her at the Upper Hutt train station.
A neighbour then saw him in Ms Donnelly's Ebdentown St flat about 5.30pm. Tamaka said he would leave, and was later heard knocking at the door about 11pm.
Justice Young said Tamaka had killed Ms Donnelly by putting his hand or forearm across her throat and applying "significant pressure".
Tamaka then attempted to disguise the events and dispose of evidence.
Justice Young pointed to aggravating features, including Ms Donnelly's vulnerability due to her intellectual disability, and a "sexual element" to her killing.
A psychiatric report painted a bleak picture of Tamaka's troubled past and history of previous offending.
He was deprived of oxygen at birth, which had left him with a degree of intellectual impairment. He had also suffered violence, sexual and emotional abuse, and substance abuse.
His previous convictions included dishonesty, indecent assault and injuring with intent.
Defence lawyer Kevin Preston said Tamaka had a "constellation of problems" but was motivated to improve and change his ways.
He regretted what he had done, and wanted to meet Ms Donnelly's family, but respected that they did not want to.
- Matthew Backhouse of APNZ