REMOVE stems and part of inner parts of strawberries to form a small bowl. Cut a sliver off of bottom of each strawberry so that strawberry will stand on end; discard slivers.
PLACE morsels and cream in small, microwave-safe bowl. Microwave on HIGH (100%) power for 30 seconds; stir until creamy. If necessary, microwave at additional 10-second intervals, stirring just until morsels are melted. Let cool slightly.
PLACE cream cheese and powdered sugar in large mixer bowl. Beat until creamy; beat in chocolate mixture.
PLACE cream cheese mixture in large pastry bag with star tip or spoon into gallon-size heavy-duty plastic bag with a 1/4-inch-wide opening cut at one corner. Pipe mixture into strawberry cups, filling cups completely and then mounding mixture on top of each strawberry. Refrigerate for at least 1 hour. For best flavor, consume within 24 hours.