A natural gas water heater was used accidentally for a few months when propane was the gas source. Is the natural gas water heater damaged or if so, repairable? Does propane gas burn hotter than natural gas and could running propane gas though a natural gas water heater damage it and become a danger if used once again, but, with natural gas.
Propane contains more energy than natural gas (NG), and its usually delivered at a higher pressure. Propane orifices (the small hole that meters the gas output) are normally smaller than NG because of this. Connecting an NG appliance to propane means you're using a lot more gas that you should, and the appliance will burn hotter.
Many appliances have overheat protection to shut off the gas before they are damaged, but if the water heater was used for a long period of time, I would be worried about the many cycles of heat that are higher than they should be for the design.
So, with that background out of the way, I have to admit I really don't know what happens in practice when a NG water heater is connected to propane, but most documentation says it will get too hot, and while it seems to have worked for months, and may continue to work, I'm not sure I would trust it to keep working on NG or converted to propane. If its in an area like a garage where a burst tank wouldn't be that bad, maybe you could use it, but honestly I wouldn't take a chance without disassembly, inspection, and replacement of any parts that could have overheated. Even then the metal of the tank could be fatigued beyond its useful life.