That is a dumb idea.
The business and people should just move. If weather patterns are changing, it would be far less costly to accommodate the Earth, than the reverse.
As quickly as we pump the water out there? It will evaporate in the heat or be used up by growing population. It is a waste of energy and the resources. Fresh water, in an increasingly crowded world, with increasingly higher living standards for everyone, should be conserved, not pumped into climates that are not suitable.
You write like, oh, just shift water resources, like it would not affect that places or environments or ecosystems where those resources currently are. . . but it would.
Various regional governments, are not just going to agree to pump water, which those ecosystems depend on, to environments which will just use it up that resource, and STILL be in the position that they are in. . . .