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So to clarify is the mod on the Series 1 using a Mini pump the same as the BMW pump being used on the Series 2 onwards?
Kind of...on S2/3
Different rack, different plumbing, different wiring
But yes, just the same.....

S4 onwards is (I believe) using the engine driven pump not electro-hydraulic
The MINI pump is no longer available new (although I do have a limited supply), there are also a couple of generations of the MINI pump and you need the right one, also a couple of the plumbing connections are unique
Simon @ SiFab.co.uk