Put the cream cheese in a large bowl and beat with an electric mixer until soft. Add the cream, confectioners' sugar, preserves, lemon juice and vanilla, and beat until it just holds stiff peaks.
Arrange about a third of the graham crackers on the bottom of a 9-by-13-inch baking dish (or a loaf pan plus an 8-inch square baking dish), fitting in as many as possible without overlapping. Spoon a third of the cream mixture on top and smooth evenly with an offset spatula. Arrange a third of the strawberries on top in a single layer. Repeat to make three layers of each. Put the remaining graham cracker in a resealable plastic bag and crush it to make crumbs. Sprinkle the crumbs all over the cake. Cover with plastic wrap and refrigerate until the cookies soften, at least 4 hours but preferably overnight.