1. In 12-inch skillet over medium heat, in hot butter or margarine, cook mushrooms until tender. Stir in bread crumbs, cheese, egg, and 1/2 teaspoon salt. Remove from heat.
2. Cut each hen in half. Rinse hens with running cold water and drain well. Carefully loosen skin on. each hen half by pushing fingers between skin and meat to form a pocket, being careful not to rip skin. Spoon some stuffing into each pocket. Fasten skin with toothpicks.
3. Wipe skillet clean. In same skillet over medium-high heat, in hot salad oil, brown hen halves, stuffing side down; then carefully turn halves and brown other side. To hens in skillet, add bouillon, water, thyme, and 1 teaspoon salt; over high heat, heat to boiling. Reduce heat to low; cover and simmer 15 minutes, basting hens occasionally with liquid in skillet.
4. Skim fat from liquid in skillet. Add rice; over high heat, heat to boiling. Reduce heat to low; cover and simmer 10 minutes, stirring occasionally. Add green beans, separating beans with fork. Cover; continue cooking 10 minutes or until rice and beans are tender.