Combine the cider, juice, sugars and cinnamon sticks in a large sauce pan. Over medium heat, bring to a boil. Turn off the heat and let it cool to room temperature. Stir in the moonshine. Pour into mason jars (you can strain it with a coffee filter if you'd like to make it more clear.)
It's ready to drink now, but it gets even better with age!
Makes about 2 1/2 quarts.
With the alcohol, this keeps almost indefinitely. However, I try (and almost always succeed) in drinking it up within a year