The current cables would be too long for this conversion and so would the S-Type cables as you would be setting the handle bar lower than they are even on an S-Type. You might after some careful measuring be able to cut down the existing cables to suit.

I have a bespoke S-Type and love the riding position.... I also bought my Dad a Brompton... he wanted an S-Type but none of the dealers had one in stock and he wanted one there and then (he just will not wait haha)....I looked at doing the conversion from M to S and to do it properly you need the S-Type handlebars, stem, cables and I think IIRC also the brake levers.