Fuel pump or not

Shutting off while driving but starting again once it cools off usually is not a fuel pump, it is normally a bad sensor that is heating up. It could be a crank sensor, cam sensor or one of the others. Only real way to tell is to scan it with a good scan tool and see what the system is doing when it shuts down.

Does it seem to shut down faster if the engine is already warm instead of cold from being parked overnight? When it shuts off is it sputtering or just like you turned off the key?