Line 13 x 9 inch pan with some of the graham crackers, breaking crackers if necessary. Pour cold milk into bowl. Add pudding mix. With electric mixer at low speed, beat until well blended, 1 to 2 mins. Let stand 5 min, then blend in non dairy whipped topping. Spread half of the pudding mixture over crackers. Add another layer of crackers. Top with remaining pudding mixture and remaining crackers.
Spread pie filling over crackers. Chill about 3 hours.