Put the cream cheese and preserves in a small bowl and mix until thoroughly combined.
Lay out the tortillas and place a quarter of the cream cheese mixture into the center of each, spreading the mixture out so there is a 3/4-inch border around the edge. Fold in 2 of the opposite sides of each tortilla and roll to form a small burrito. Set aside.
Combine the sugar and lime zest on a small plate.
Heat 1 inch of the vegetable oil in a large skillet to 325 degrees F. Carefully fry the chimichangas until golden, 1 to 2 minutes per side. Remove from the oil and toss in the lime sugar.
Serve immediately, topped with the berries and whipped cream. Accompany with some extra preserves on the side.