TOSS berries with sugar; cover. Refrigerate 30 min.
MEANWHILE, add whipped topping to jam in medium bowl; stir with wire whisk until well blended. Cover and refrigerate until ready to use.
PLACE 1 cookie on each of 6 dessert plates; cover each with 2 Tbsp. of the berry mixture. Drizzle evenly with any remaining berry juices. Top each with 1 Tbsp. of the whipped topping mixture. Repeat layers. Top with remaining cookies and whipped topping mixture. Refrigerate at least 15 min. before serving to allow cookies to soften.