Get a contract. Either write it up yourself or hire a lawyer to do it. You can find free templates online and just modify to fit your needs. Make sure that both parties sign it, and that both parties get a copy of it with both signatures on it.
Try to determine how long it will take you to translate this thing, in terms of hours spent actually working. Do some research to see if there is even any demand for this book. If you spend 100 hours rewriting this book, and it gets only 50 sales at $20 a pop, that's $1,000 you get half of, so you're working under US minimum wage at that point.
Know that doing a no-upfront deal is risky in itself. I have been burned on that before, multiple times sadly. One of them was recently, a guy who ran a startup, and had the startup mentality, and wouldn't pay me what I was owed for reputation management work until months after the invoice was due, because I got paid after his investors paid up. I didn't want my income tied to the salesmanship of his startup, and after over a year got sick of chasing him for invoices, so I cut ties.
I suggest requesting some form of money upfront, to ensure that your client is actually serious about this project, or if this is simply a joint venture where the other party hands all the actual labor off to someone else (you) and then walks away with 50% simply for selling the thing.
People have a tendency to not give a shit about something if they don't have to put their money where their mouth is to make a working product.