Set aside three strawberries for garnish; slice the remaining strawberries. In a large bowl, whisk milk and pudding mix for 2 minutes. Let stand for 2 minutes or until soft-set. In a large bowl, beat cream cheese until smooth; gradually beat in 2 tablespoons coffee. Beat in pudding. Fold in whipped topping.
Brush remaining coffee over ladyfingers. Line the bottom of a 3-qt. trifle or glass serving bowl with half of the ladyfingers. Top with half of the sliced berries, grated chocolate and pudding mixture; repeat layers. Cut reserved berries in half; place on trifle. Cover and refrigerate for 4 hours or overnight.