Agreed with this. What is it housed with currently? You'll find that if theres any stress/aggression/nipping from other inhabitants that it will hugely prolong the healing process.
It's hard to tell from photos just how serious/permanent the damage is as both 'sections' of the caudal fin will be swaying and bending differently in the water. From that photo though it looks like both the top and bottom soft rays are bending away from the tear, but that is more than likely the angle.