The Brompton sub frame (rear triangle) has a spacing of ~120mm which the 3 spd hubs fit in. Other IGHs tend to fit frames with 135 mm spacing although there are owners who have widened the rears of their Brommies and installed 7+ speed hubs but that compromises the bike's folded size to a small degree.

Before deciding on the 6 speed consider that it uses the BWR hub, which is entirely different than the BSR (similar to the AW) used on the 3 speeds, and replacement parts are limited for the BWR yet plentiful for the BSR. Also the jumps between gears on the 6 speed are fairly large, so much so that I personally prefer the route of adding a double chainring crank and front derailleur to my 3 speed that allows for closer gear ratios which are more usable to me.

Stock Brompton gearing:


Double chainring gearing (50/44 X 14):




Just food for thought.