In a blender or food processor, combine berries, sugar, and lemon juice; blend until smooth. Pour mixture through a fine-mesh sieve, pressing with a rubber spatula to discard the seeds.
In a mixing bowl, combine the heavy cream and confectioners’ sugar. Use an electric mixer to whisk until peaks form.
Fold ¾ of the blackberry puree into the whipped cream gently.
Pulse the shortbread cookies in a food processor until they form coarse crumbs. Alternatively, crush them in a ziploc bag with a rolling pin.
Serve the blackberry fool in decorative glasses or bowls. Top with remaining berry puree, cookie crumbs, and additional blackberries.