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Ms Lukins, 39, was at the Mangere Lawn Cemetery and Crematorium on Sunday when her baby bag, containing a camera with images of her daughter's first four months, was stolen.
"It's just really sad for me. Babies change so much. I just keep thinking back on all the photos I've taken and thinking I'll never see those again."
Ms Lukins has lived in Britain for the past 17 years and has been back in New Zealand on maternity leave for almost four months after the birth of her daughter, Claudia O'Donnell, who is almost 5 months old.
"I can't even believe it. There would have been hundreds of photos, I've been taking so many. It was her first Christmas, her first trip to New Zealand, we'd been to the beach for the first time. I know those photos won't mean anything to [the thief].
"I can't really describe what it would mean to me to get the camera back. I really don't care about anything else in that bag, I can replace all that but I can never get those photos back."
The mother was showing her grandmother's grave to her baby in Mangere, after visiting her father's grave in Manukau. She was with her elderly mother, Colleen Lukins.
She never expected to be robbed in a cemetery. They only ventured about 25 metres from the car, she said.
"We had flowers and were putting them on my grandmother's grave. I was carrying [Claudia] and mum walks with a limp. I feel like they probably saw us and thought, perfect, they won't even notice.
"I didn't see anything, I didn't hear anything. It's just a bit sick."
Stolen in the bag were the camera, her purse, house keys, her mother's cellphone and baby clothes. They have already had the locks on the house changed.
She realised she should have backed up the photos on to her computer, and had planned to do so over the weekend.
Counties Manukau West prevention manager Acting Inspector Dave Glossop said nothing was sacred for some thieves, and they would take advantage wherever they could.
"Cemeteries don't stand out as a place that's particularly targeted, but people need to be vigilant make sure anything of value is left out of sight."
Mr Glossop said he would like the camera returned to Ms Lukins, even if it was done anonymously.
The camera could be dropped into the police station, or posted, he said.
"Find a way to get it back into the authorities' hands, and we can get it back to the lady."
- Sam Boyer, NZ Herald