The water boiling one doesn't make any sense. One of those devices (stove or kettle) transfers more heat per unit of time into the water. Just use that device for the full amount of water.
An induction range would remove the need for transferring boiling water around. At least in the US, that's the fastest device, since countertop kettles are limited to 1.8kW or so. Induction 'burners' usually are 2.5-4kW, and assuming the right cookware, much better at transferring that energy into the water (and not the air like a gas burner)