Preheat oven to 375 degrees. Make filling: In a medium bowl, stir together spinach, ricotta, garlic, teaspoon salt, and 1/4 teaspoon pepper; set aside. In another medium bowl, stir together tomato sauce and prosciutto.
In an 8-inch square baking dish, spread cup tomato sauce. Layer 2 noodles, 1/3 filling, and 1/3 remaining tomato sauce; repeat twice. Top with mozzarella. Bake until browned, 35 to 40 minutes. Let stand 5 minutes before serving.
It's important to squeeze the thawed spinach dry, or the lasagna may be watery.