After Faulkner arrived Mills shot him in the chest with a gun he kept loaded in the laundry.
Faulkner wasn't killed immediately and was able to wrestle the firearm from Mills before fleeing from the house but collapsed and died.
Mills, who was on bail for burglary and firearms offences at the time of the shooting, pleaded guilty to murder and possession of a firearm.
He appeared before the Parole Board for the second time in May 2022.
The board noted Mills had a record of misconducts in prison but his conduct had significantly improved and while initially refusing to complete a drug treatment programme he had finished it after being transferred from Whanganui Prison to Hawke's Bay.
"He has had very good reports from both the Dependency Treatment Programme and the Medium Intensity Rehabilitation Programme and it is very positive to see the work that he has done on his rehabilitation," board chair Sir Ron Young said.
Mills, who had previously done some engineering work and had a qualification as a lab technician, had completed all of his rehabilitation treatment, and his lawyer Debbie Goodlet sought parole.
The board, however believed Mills remained an undue risk and needed to do some reintegration work before he could be safely released.
"The way forward, we think, for him is for guided releases, outer self-care and release to work.
"Doing well in all of those areas will illustrate that he can function well in society and that we can be confident that the rehabilitation programmes he has undertaken have made a significant difference to his conduct."
The board would next consider Mills for parole before the end of February 2023.
Parker was initially charged with being party to murder but later pleaded guilty to manslaughter during her trial and was sentenced to six years and four months' jail.
