She was sentenced to life imprisonment with a minimum period of 13 years for the murder of Mr Watene in the small Southland town of Otautau on April 16, 2020.
Today the Court of Appeal confirmed Graham had appealed her conviction and sentence.
At sentencing Justice Gerald Nation said the killing and cover-up was callous and merciless.
Graham’s cover-up included telling one of her children Watene was playing dead on the night in question.
She recruited her friend George Hyde to help her first hide, then dispose, of Watene’s body while pointing the finger at other possible suspects.
Hyde narrowly avoided a jail term for his role in the cover-up of the murder, instead receiving a sentence of eight months home detention.
It was revealed in court that while digging Mr Watene’s grave with Hyde, her children played nearby.
She also sent messages to Mr Watene’s mother Christine, saying she would let her know if she heard anything about his disappearance.
Mr Watene’s body was found a month after his death - buried in a shallow grave in the Longwood Forest, covered in rubble that came from Hyde’s house.
She claimed the killing took place during a heated argument between Mr Watene and Graham and that the gun went off accidentally during a struggle for the weapon.
It wasn’t until she got to trial that Graham claimed the shooting was accidental; however, she was unable to recall who pulled the trigger.
The cover-up, she said in evidence, was because she was scared she would lose her children to Oranga Tamariki.
A hearing date has not yet been set for the appeal.
