Whisk preserves, 1/3 cup Cointreau, and orange juice in 2-cup measuring cup. Place mascarpone cheese and 2 tablespoons Cointreau in large bowl; fold just to blend. Using electric mixer, beat cream, sugar, vanilla, and remaining 2 tablespoons Cointreau in another large bowl to soft peaks. Stir 1/4 of whipped cream mixture into mascarpone mixture to lighten. Fold in remaining whipped cream. Hull and slice half of strawberries. Spread 1/2 cup preserve mixture over bottom of 3-quart oblong serving dish or a 13x9x2-inch glass baking dish. Arrange enough ladyfingers over strawberry mixture to cover bottom of dish. Spoon 3/4 cup preserve mixture over ladyfingers, then spread 2 1/2 cups mascarpone mixture over. Arrange 2 cups sliced strawberries over mascarpone mixture. Repeat layering with remaining lady fingers, preserve mixture, and mascarpone mixture. Cover with plastic and chill at least 8 hours or overnight. Slice remaining strawberries. Arrange over tiramasu and serve. *Italian cream cheese available at supermarkets and at Italian markets.