Put glasses in a cool place. Wash the lime with hot water, grate dry and peel the lime in fine pieces. Squeeze lime. Wash the strawberries and dab dry.
Crush half of the ice cubes in a mixer. Add syrup, lime juice, rum and strawberries, except 4-6 pieces, and puree. Add remaining ice cubes and puree again. Depending on taste, add some more syrup, lime juice or rum
Cut the remaining strawberries from the tip. Spread the cocktail on glasses and decorate with lime peel and strawberries