Wash the lime, grate it dry and peel the rind into strips with a zest ripper. Halve the lime and squeeze the juice. Peel the ginger and chop it into small pieces. Cover about 1/3 of the lime zests with a damp cloth.
Bring the remaining lime zests, ginger, lime juice, 4 tablespoons of water and sugar to the boil and simmer for about 3 minutes. Pour the ginger syrup through a sieve and let it cool down lukewarm.
Wash, clean and quarter the strawberries. Sort raspberries. Wash blackberries and currants and drain well. Strip currants from the panicles. Carefully mix the berries with the lukewarm ginger syrup and chill for about 1 hour.
Decorate with remaining lime zests before serving. Dust with icing sugar if necessary. Whipped cream tastes good with it.