snatch steal

This brings up I question I encountered at a tournament a few weeks ago. I think I know what happens, but I might be wrong so correct me if I am wrong

A player controls a monster (any monster except Blindly Loyal Goblin or Mataza) and his opponent activates Snatch Steal. Both players agree to let this resolve, so the opponent gains control of the monster. Then, the opponent who now controls the monster Book of Moons it. Snatch Steal is destroyed, but doesn't the monster stay under the control of the opponent?
 
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