No, 'established' does not work there, and neither does your sentence. You can use these: This movie is based on a true story. - - This is the only natural way to say it.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
Mister MicawberThey/The producers/ The screenwriter based this movie on a true story.Yes! Thanks Sir that is the sentence that pulled me through the confusion.