"How would share prices react to high inflation Would they move up considerably?"
what you saw at the first half of 2008 is precisely what you'll see again during a inflationary environment arising out of cheap money. Flight to commodities and resources, gold, silver, oil and energy.
Did anyone happen to notice commodities made their largest gains after the Bear Sterns bailout by the Fed (first signs of money printing and devaluing the USD).
Since that time many other central banks have joined in and are all essentially in the same boat. I don't think you can truly say one currency is better than the other right here right now. They're all flawed. However the move that we saw in commodities post Bear was still linked to demand. Demand has since come back due to lack of banks lending.
This will return in time IMO. And when it does people will start speculating like crazy with all those free dollars being printed around the world.