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Yes, they will fit. I know that there are two different Cooper S shocks (sport and base). My car had the sport suspension, and the shocks have a paper label on them, saying 'cooper S sport'. I put non-sport shocks on them, labeled 'cooper s'. I don't know if the shocks on a base cooper are identical to the S shocks or not.
So, they may be different internally, but they will bolt up.