In April, Molloy was fined $15,000 and sentenced to 350 hours of community work for the breach.
Here's what we know.
They say the stress contributed to David Millane's early death.
Kempson's former partner described him as "volatile", "scary" and "manipulative".
He will spend at least 17 years in prison for the British backpacker's murder.
The killer will be thrust back into the spotlight when name suppression ends and that is unfair, writes Mark Longley
David Millane died in the UK earlier this week.
UK backpacker Grace Millane was killed in Auckland in November 2018.
The killer's lawyer said the appeal wasn't about condoning his actions after the woman's death.
He was found guilty in November of murdering the woman.
"Changes need to be made to protect women."
He was convicted of her murder last year.
The campaign is in its final push for donations as it finishes tomorrow.
The appeals runs until March 6.
Detective Inspector Scott Beard says the man jailed for her murder would have killed eventually.
He says it was the duty of the defence lawyer to put it forward.
The judge also explained what life imprisonment really means.
"One person has been locked away but are New Zealand women any safer?"
"Strangling someone for five to 10 minutes until they die is not rough sex."
The killer's fate has been revealed by Justice Moore.
Beard was at the forefront of the police investigation into Millane's death.
The British backpacker was murdered in December 2018.
“Your barbaric actions towards my Grace is beyond comprehension.”
Eight extra drop-off locations were added overnight.
The charity has already received hundreds of messages of love and support.
Love Grace gives handbags filled with essentials to women who leave violent situations.
"The message is clear. Get a check-up. It's a simple blood test."
The Tenancy Tribunal has made the order.
He is thought to be the first person charged with breaching name suppression in the case.
He is the first person arrested in relation to the court suppressions.
"The comments made in this video are offensive and would be extremely upsetting."
We don't do a good job in New Zealand of facing the reality of men's violence against women.
Why does Grace Millane's murderer still enjoy privacy when the details of Grace's life have been dragged through the courts?
UK families who have loved ones murdered in the UK or EU countries can apply for a payout
After nearly a year, her family finally got justice.
It says the 'rough sex gone wrong' defence is incredibly concerning.
Police say it's still an offence to name him on social media.
We can all learn a thing or two from the way the parents behaved, writes Mark Longley.
"Many people would say that effectively blackens her character."
"Doing nothing is one option that is not open."
"Grace was our sunshine and she will be missed forever."
The British backpacker came to New Zealand in November, 2018.
After a three week trial, the jury have handed down their verdict.
The jury delivered its verdict on Friday.
The case will be summed up by Justice Simon Moore on Friday.
The defence has finished its closing summary by telling the jury Millane's death was tragic, but not a murder.
The defence has wrapped up its case, with closing statements expected on Thursday.
A high level of alcohol was likely in her blood, a pathologist says.
The murder-accused may enter the witness box.