A 22-year-old man told police he murdered a school friend's mother in her Melbourne home over a lost public transport travel card, court documents have revealed.

Papua New Guinea national Sigarah 'Steve' Baea has pleaded guilty to killing Prasad Somawansa, 48, while she was home alone in Hoppers Crossing last February.

He confessed to the crime to police, telling them he got angry when she would not let him in to look for his Myki card.

"I told her I wanted to get my Myki card and then she ... told me to piss off," he told police.

"I got angry and I stabbed her, then I went up to get my Myki card but it wasn't there."

Court documents also revealed Ms Somawansa's husband of 22 years heard her last moments over the phone after calling her from Brisbane where he had just arrived for work.

"I could hear my wife speaking but not to me," he told police.

"I heard her saying; 'you go out, you go out, you go out' ... she sounded scared as she said this.

"I heard her yelling ... and then making loud deep breathing noises before the phone was cut off."

Mr Somawansa tried to call her back but she did not answer.

He asked a friend to go over to the house to check on his wife but she was found dead in the lounge room with her phone next to her.

Baea had been a friend of Ms Somawansa's son Wishhasad in primary school but the pair had not seen each other for nine years until a month before the murder.

They bumped into each other and had begun hanging out which they were doing the night of Ms Somawansa's murder.

When Wishhasad was called out on a job with the State Emergency Service he dropped Baea at a nearby shopping centre.

But the Baea told police he returned to the house in search of his Myki card.

Wishhasad told police he had not wanted Baea to come over that day and did not trust him to stay at his home.

"Steve seemed pretty nice but he seemed violent," he said.

"Anything that he talked about he resorted through violence by beating people up.

"He smiled and he laughed but the words that were coming out of his mouth didn't match his appearance."

Baea will appear in the Victorian Supreme Court on Friday.