Prepare the popcorn shrimp according to the package directions for the air fryer.

Bring 1/2 cup water to a simmer in a small saucepan over medium-high heat. Stir in the rice and 1/2 teaspoon salt. Return to a simmer, cover with a tight-fitting lid and reduce the heat to low. Cook until all the water is absorbed and the rice is tender, about 15 minutes. Remove from the heat, let stand covered for 5 minutes and fluff with a fork. Stir in the cilantro and lime zest.

Wrap the flour tortillas in a damp paper towel and microwave until warm and pliable, about 30 seconds. Place the tortillas on a cutting board or clean work surface. Using a small offset spatula or the back of a spoon, spread 1/4 cup of the refried beans in the center of each tortilla in a rectangular shape. Top with 1/4 cup rice, a quarter of the popcorn shrimp and 1/4 cup of the cheese.

Fold in the two opposite side of the tortilla over the filling. Fold the side closest to you over the filling, then tightly roll the burrito away from you. Place the chimichanga seam-side down and brush the top and bottom with olive oil. Repeat with the remaining 3 tortillas.

Preheat the air fryer to 390 degrees F. Place the chimichangas in the air fryer basket seam-side down (see Cook's Note). Air fry until golden brown and crisp all over, 5 to 6 minutes. Sprinkle the remaining 1/2 cup cheese on the top of the chimichangas, then air fry 1 minute more to melt. Serve with shredded lettuce, pico de gallo, diced avocado, sour cream and lime wedges