1. Bring water to boil and add rice. Just before all the water is absorbed, add 1 cup rice milk, sugar, salt and cinnamon. Continue to boil on low until thick and creamy.
2. Combine beaten egg and 1/2 cup rice milk.
3. Add to rice mixture and stir continually until the pudding is very thick.
4. Remove from heat and add margarine and vanilla. Dish into serving bowls and serve warm, or cover with plastic wrap and chill in the fridge.
5. Serve cold.