He knows what he has to do. It's just more fun with mum and dad. Gets him lots of attention. Reasoning with him won't have any effect.
I wouldn't bother with a book. That's just more attention, more reward for the undesirable behaviour. Instead, his parents need to be totally boring and unrewarding. We called it The Boring Return.
1st time dc got up, one of us would take him by the hand and quietly return him to his bed, saying "It's bed time now. Dc stays in bed. Goodnight." Nothing else. And then quietly leave his room. No fuss.
2nd time he got up, same thing with even fewer words "Bed time now."
3rd and subsequent times, no speaking at all. Just quietly returned to bed.
First night would take several returns, maybe over as long as an hour. Subsequent nights would take less and less time, fewer returns. Never took longer than a week to establish that dc stayed in bed. Any changes, like redecorating the bedroom, often meant we needed to do the Boring Return again, but it never took as long the first time.