In 2-quart saucepan, stir 11/2 cups of the milk, the cherries, brown sugar, butter, cinnamon and salt. Heat to boiling over medium heat, stirring occasionally. Stir in rice; reduce heat to low. Cover; simmer 5 minutes, stirring occasionally.
Meanwhile, make pudding mix as directed on package, using remaining 2 cups milk. Stir prepared pudding into rice mixture. Serve warm. Garnish with cinnamon sticks.