Combine water and mushrooms; cover and let stand 20 minutes. Drain, reserving 1/2 cup mushroom liquid. Discard mushroom stems. Thinly slice mushroom caps. Combine mushroom caps, the reserved mushroom liquid, chicken broth, sherry, soy sauce, and pepper in a medium saucepan; bring to a boil. Slowly drizzle egg into soup, stirring constantly with a fork. Reduce heat to low, and cook an additional 1 minute, stirring constantly. Ladle into individual soup bowls, and top with green onions.