Combine cranberries, 1 1/2 cups water, sugar, ginger, and shallot in heavy large saucepan. Stir over medium heat until sugar dissolves. Cover and cook until berries burst, about 10 minutes. Stir in molasses. Season with salt. Cool. Cover and chill until cold, about 3 hours. (Can be made 1 week ahead. Keep refrigerated.)
