In a medium saucepan combine mangoes, water, sugar, tapioca, lemon juice, and ground ginger. Bring to boiling; reduce heat. Cover and simmer for 10 minutes, stirring often. Remove from heat. Set aside to cool slightly.
Fold half of the raspberries into mango mixture. Pour into pastry shell. Arrange remaining berries on top. Cover and chill for 4 to 24 hours or until set.
If desired, serve with whipped cream. Makes 8 servings.