Preheat oven to 350°. In a large skillet, saute mushrooms in butter until tender. Add garlic; cook 1 minute. Add artichokes, wine, salt and pepper; cook over medium heat until liquid is evaporated.
For sauce, in a large saucepan over medium heat, melt butter. Stir in flour until smooth; gradually add milk. Bring to a boil; cook and stir 1 minute or until thickened. Stir in Parmesan cheese and wine.
Spread 1 cup sauce into a greased 13x9-in. baking dish. Layer with 3 noodles, 1-2/3 cups sauce, 1 cup mozzarella and 1-1/3 cups artichoke mixture. Repeat layers twice. Cover and bake 45 minutes. Sprinkle with remaining mozzarella cheese. Bake, uncovered, until cheese is melted, 15-20 minutes. Let stand 15 minutes before cutting.