Spread the coconut onto a large sheet of baking paper.
Cut each half of the sponge cake in half horizontally and spread 2 of the halves with the jam. Top with the remaining halves, then cut each jam-layered sponge into 8 filled portions.
Sift the icing sugar and cocoa powder into a bowl. Add vanilla and gradually add enough warm water to form a slightly runny icing. Dip each cake portion in the icing to coat completely (be warned, this is a messy job. You may want to wear gloves). Roll each piece of cake in the coconut, then place on a wire rack for 15 minutes to dry before packing in plastic containers.