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