If you are convicted of killing a specific Bob Shire and serve your sentance, then later you find out that specific Bob Shire is living the good life you could walk right up to him and rip out his still beating heart and not be tried again. Why? Double Jeopardy. You were already tried and convicted for Bob Shire's death.
As was already explained, and contrary to what they tell you in that stupid movie, double jeopardy would not apply because you are being accused of a different instance of the crime. It's the same offense and has the same victim, but it's still a new instance. Obviously charging you with murdering someone again is implicitly admitting that your first conviction was wrong, but that doesn't change the fact that it's still a new instance of the crime. Much like robbing a bank a second time is a new instance of a crime, even though it's the same crime and same victim.