Yes, the hub is identical
Same 5x112 PCD and same 66.5 mm centre bore: wheels from BMW 2 Serie Active Tourer U06 bolt on and centre on Mini Cooper S without rings. You still need to check the offset and tyres, detailed below.
≈: width estimated from the original tyre size.
Wheel by wheel: offset and tyres
Each original wheel from BMW 2 Serie Active Tourer U06 is compared with the one from Mini Cooper S of the same diameter: how much closer the wheel gets to the shock absorber or how far it sticks out of the wheel arch, and whether the tyre keeps the same overall diameter.
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≈6.5Jx16 ET47 · 205/60R16 — Check on the car
Compared with the original ≈6Jx16 ET50 on Mini Cooper S: shock absorber side +3.4 mm, wheel arch side +9.4 mm, tyre diameter +5.1 % : fit it with the original tyre size of Mini Cooper S (195/55R16), not that of BMW 2 Serie Active Tourer U06.
Comparison for guidance only (estimated width). Check in detail
Before fitting the wheels
An identical hub is not enough: offset, width and diameter change the position of the wheel, and larger calipers can touch a smaller wheel. Original wheels often use bolts or nuts with a specific seat: keep the fixings intended for the wheel, with the thread of Mini Cooper S (M12x1.50), tightened to the torque shown on its vehicle page. Finally, check that the size is among the approved fitments for your vehicle. This comparison is for guidance only: have the fitting approved by a professional.
And the other way round: wheels from Mini Cooper S on BMW 2 Serie Active Tourer U06?