And let's say he somehow manages to replace the money, either by means of borrowing or working menial jobs to raise the money, will his parents ever trust him again to save large sum of money with him?
Just as the parable goes,
"It will be easier for a camel to pass through the eye of a needle, than for this boy's father to ever believe him with entrusting a large sum of money again". Because as it stands now, it's very visible that trust has been broken, and when it's broken, it only takes time to get heal of it. Hence, I think the only advice I can give him now is to stop gambling with people's money and ask for forgiveness from his parents.
Assuming you find yourself in a similar situation as this, what will you do? How will you handle the situation to make your parents trust you again?
If I was to find myself in this shoe, I think the best to do is to sincerely ask for forgiveness and stop gambling with other people's money.