How can there be two Frozen Flame, or rather, WHAT is the Frozen Flame in Chronopolis? Isn't it the original?

I believe that there is only ONE Frozen Flame and it was used by Fate. When FATE died, the Dragon Gods obtained the same Frozen Flame from Chronopolis and placed it at Terra Tower (aka Dinopolis). I do not remember any dialouge evidences that the one in Chronopolis is fake.