Jamie Lee Warn (55) denies murder and two counts of perverting the course of justice by lying to the police.
Jurors were told that on 10 May last year Miss Besenyei made a hair appointment with Eclipse Hair Design for the following day, but she failed to attend.
The Crown contends she has been killed on 10 or 11 May by Mr Warn.
The court also heard from her former landlord, Trevor Lucas, who said she rented a small single room in a house shared with two others in the months before her death.
He said the rent was paid in cash every Friday – first at £100 a week and later it went up to £120.
He recalled last seeing Miss Besenyei on the evening of Thursday, 10 May.
He said he did not see her again, in spite of the rent being due on Friday. He told the court he sent her a text on the Sunday chasing the rent.
Later that day he received a text, purportedly from her, saying she was sorry, and would sort it out when she saw him.
‘It did not sound like her at all,’ he told the court. ‘It was not her way of texting me.’
But he said he did not think about it further until the police knocked on his door the next day, saying Miss Besenyei’s car had been found and she was now a missing person.
The Crown alleges that Mr Warn murdered the 37-year-old and hid her body in the boot of her car for three days. He then dumped her remains at Le Pulec Bay and drove her car onto the beach at St Aubin to make it look as though she had taken her own life.
The prosecution claim that at various points after the alleged murder Mr Warn also sent text messages from Miss Besenyei’s phone to make it look as though she was still alive.