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A ripped up card reading 'There's surveillance cameras inside and outside the house' was found in the pocket of a woman who plunged to her death from her 15th storey apartment, a Sydney court has heard.

Lisa Cecilia Harnum's fiance, Simon Gittany is accused of killing her, with prosecutor Daniel Noll describing him as a "jealous" and "domineering" man.

"I think it's that she had it in her pocket to warn people," Mr Noll said. "That demonstrates the consciousness of the surveillance the accused subjected the deceased to and was a hallmark of the jealous and controlling relationship."

On Thursday, the court heard Mr Gittany installed cameras to see who was at the door. On July 30, 2011 Mr Noll said the victim and her fiance began arguing because Ms Harnum threatened to leave Mr Gittany.

"[Mr Gittany was] enraged by the actions of the deceased in attempting to leave him and the accused carried her to the balcony and dropped her from the 15th floor."

Lisa Harnum's mother told the court her daughter reached out for help, asking her to come from Canada to Australia, the day before her death.

"Lisa said to me, 'Mommy can you please come and get me?' I said, 'I can come this Friday August 8, can you hang on till then?'

"I wish now I had just dropped everything and ran to her."

Mr Gittany refuted the claims to police.

"I was in the kitchen and I saw her run past to the balcony. I remember thinking, 'What's on the balcony?' I saw her step over the railing onto the little cliff face," he said.

"I was just grabbing her. I might have had her handbag or jacket and then she was gone."