Whisk preserves, ⅓ 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 ¼ of whipped cream mixture into mascarpone mixture to lighten. Fold in remaining whipped cream.
Hull and slice half of strawberries.
Spread ½ 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 ¾ cup preserve mixture over ladyfingers, then spread 2 ½ 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 tiramasù and serve.
