All alloys from first and second generation Minis will fit each other, providing they are big enough to fit over the brakes. That means to fit over the brakes of a second generation Cooper S requires 16" wheels but all other cars can use 15" wheels.
So your 07 One (second generation) alloys will fit an 02 Cooper S (first generation). The actual wheel studs are different in the two generations but the holes in the wheels are the same for both, so the studs stay with the car.
Whether it is a good idea to put One wheels on a Cooper S is another matter. If it is for a gentle driver, then that's probably OK, but if the Cooper S driver uses all the power, then the tyres on basic One alloys (probably 15" unless they were 'up-specced') may be a bit small.
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