Puree the kiwis with sugar, white rum, lime juice and crushed ice in a blender or hand blender.
Shake the strawberry juice with the brown rum, lemon juice and ice in the shaker.
Pour the kiwi mixture into a large glass, it should be as thick as possible, if necessary you can put it again in the freezer compartment beforehand. Carefully fill up with the mix from the shaker.
Serve garnished with a lime wedge and a sprig of mint.