Energy is conserved. It becomes the the dynamic energy of the water molecule.
Water in a hydroelectric dam has potential energy that came from the Sun's energy evaporating it and raising it up from the oceans. The energy is released by running the water down a chute so that it gains kinetic energy which drives a water turbine and that drives an electric generator.
Solids can be change into liquid by melting for example the ice. It will melt by just minutes in exposure of sunlight.. Liquid can be turned to gas by evaporating. Example a water can evaporate when heated..... :)
It should be noted that energy cannot be gained or lost due to energy conservation. But there is a bit more to this as regards the situation being asked about. In terms of the energy of the water vapor, yes, the water vapor has more energy after it has evaporated. It has to have to have evaporated. The water vapor leaves the water from which it came with less energy; it took energy with it to evaporate. Either way, energy has been transferred from the body of water to the water that is evaporating, and it might help to view what is happening in that light.
Most of it will end up in the water It travels through the water.
evaporation
During evaporation water absorb thermal energy from the environment.
The evaporated water forms clouds.
You think probable to the thermal energy.
The liquid water is transformed in a gas (vapors).
Its molecules become heated.
Water energy is produced when you use the movement energy of running water to power a waterwheel. That waterwheel then powers a generator which makes electrical energy. Then the generator transfers that energy to the power station.
Evaporation is an endothermic process, absorb energy.
Salts are obtained as a residual solid.
some of the water molecules gained kinetic energy thus leaving the sea
The density of water increase, also the humidity of the atmosphere; the temperature decrease.
Water in an open system is allways evaporated.
The water is evaporating leaving the impurities behind. When condensed and recollected, it is pure water.