What can I do about my employer paying less super than I'm entitled to?

My girlfriend is on a working holiday visa here in Sydney, and is planning on claiming her super when she leaves the country as she is a temporary resident here.

She works at a small family restaurant, and while on the surface they appear to operate legally, giving her award wages and paying taxes, when my girlfriend asked told the restaurant owner about her intention to claim her super on her departure, the owner told her that he only declared her as working 2-3 nights per week, when she works 6 nights per week. He explained to her that it was better for the business that way.

I know that we are entitled to a 9% superannuation guarantee, but what can we do about it if my gf's boss IS paying the 9% SG on his falsified declared wages? On our actual earnings we have calculated that she should have around $800 of super, but depending on how little income he declared, it may drop down to $300.

Even though the restaurant pretends to operate legally, declaring wages and paying taxes, wages are paid cash in hand and no payslips are given. As such, proving how much we have worked or our total income may be difficult.

Is there anything that we can do in this situation to claim our super??

The owner declaring less wages would also mean that he must have paid less taxes for my gf. She didn't get any extra money on top of the award wage so I assume he kept that money for himself. So I'm sure that we would get less on her tax return than we are supposed to too. Is there anything we can do about that?