Washbasin faucet - cold and hot swapped!

Now it is the case that in all wall-mounted washbasin faucets cold water flows through the hot water and vice versa.

Well, if that is the case everywhere, then the plumber probably simply swapped the cold/hot water connections in the HAR. There is no need to break down drywall or tiles; this should be resolved in no time by handling it with two pipe wrenches next to the heating system.