Well, unbalancing your books is fairly irrelevant since clearly you could also do them a credit note for the balance and send that to them too leaving them to only show the invoice to their client and not the credit note.
However, by doing so you are supporting what is fundamentally fraud so on your own head be it if it comes back to you in some way if you decide to do so.
Is it normal practice? Well, I'd imagine in the real world it probably happens a lot. It's illegal though.