Cut the strawberries into pieces after washing them. You may need fewer or more strawberries, depending on how big they are. 4 were used for each glass.
Put the strawberry slices in the cocktail shaker and stir them until they are finely pureed. Also possible with a blender.
Pour the lime juice, Hennessy, triple sec, and strawberry puree into the cocktail shaker along with a few ice cubes.
Shake the shaker for one minute, or until cooled, with the lid closed.
Add 3/4 parts crushed ice to a tall glass, strain the cocktail into it, and serve.
On top of the glass rim, place a cocktail pick garnished with a lime wheel and strawberries.