Something of the sort has already happened in real life.
There was once a religion almost identical with the Jehovah’s Witnesses. It was known as the Worldwide Church of God, and it had practically identical doctrinal earmarks with the Jehovah’s Witnesses–though most of the Witnesses were unaware of it at the time.
Developed under the unorthodox teachings of Herbert Armstrong, the WCG believed almost everything taught by the Witnesses, claiming it was the one true religion. They even taught that the world would end in 1975, just as the Witnesses once did!
Unfortunately having the same doctrine is not the same as being one of Jehovah’s Witnesses, not from their viewpoint anyway. Over the years (especially since the year 2000) many of their fundamental teachings have been dismissed or redesigned to such an extent that the original religion practiced by its founding members no longer exists. Witnesses are thus not concerned about what they believe as much as they are concerned that* they *are the one’s believing what they do.
For them it’s all about belonging to their group that listens to and hangs on every word preached by their Governing Body. Unless these truths are coming from the Governing Body of Jehovah’s Witnesses, they might as well be falsehoods.
The Witnesses believe that God chose them in 1919 after the return of Jesus (which according to them occurred invisible to human eyes in October of 1914). Only the organization that grew from then is the true one and only they are being enlightened.
Besides you could never match their teachings exactly. Their theology is constantly in flux. Over the past 15 to 20 years they have gone to teaching that the world will end before the year 2000 to claiming “we will not set dates any longer for the end of the world” to the present “the world will end any day now, just watch!” Your teachings would have to change with the Governing Body’s teachings as they revise things at the very same time they revise things WITHOUT the ability to know when they make the changes and what they are for the Witnesses to accept them as “identical.” In order for you to do that would entail you having abilities far beyond normal human powers–or at least be able to bug the secret meeting of the Governing Body.
On a lighter note, the Worldwide Church of God recognized it was a cult after the death of Armstrong and made drastic changes from its leadership down. While many left, a core remained after the WCG adopted mainstream Christianity that is concurrent with those Protestant groups in ecumenical fellowship with the Catholic Church (even though I am unaware of any formal ecumenical connections between our Church and their group at this time).