Slice steak into 2 inch pieces. Brown in shortening in skillet. Pour off pan drippings. Season with salt and pepper. Drain mushrooms, reserving liquid. Add enough water to reserved liquid to measure 1 1/4 cups. Add to steak. Cook tightly covered, over low heat for 1 hour. Add mushrooms, tomato sauce, enchilada sauce, 1/2 cup onion and garlic, mixing well. Cook, covered, for 20 minutes longer. Dip tortillas in hot sauce. Place 2 teaspoons onion on one side and roll up. Arrange in 9x13 inch baking dish. Stir 3/4 cup cheese into remaining sauce. Spoon around rolled tortillas. Sprinkle with remaining cheese. Bake tightly covered, at 350 degrees F for 10 minutes or until heated through.