In large pot combine cranberries, water and juice. Bring to a boil, reduce heat, simmer covered until cranberries pop. Remove from heat and cool for 1 hour. Then transfer cranberry mixture to a blender or food processor. Cover and blend or process until smooth. Return to pot.
Add sugar and cinnamon, stir. Bring to a boil stirring constantly. Reduce heat and simmer for about 25 minutes or until mixture is thickened, stirring frequently. Remove from heat. Discard cinnamon stick.
Ladle into hot sterilized 4 oz jars, leaving 1/4" headspace. Wipe rims and add lids.
Process jars for your recommended altitude.
I like chunkier jam, so I will instead blend half the cranberries, water and juice first before cooking, then put blended berry mixer and whole berries into pot and go to step 2. Or just process all the fruit until smooth, then go onto step 2. This cuts out the 1 hour of cooling time.
If you are using frozen berries, just defrost them in cool water. Frozen cranberries last up to one year. The older they are the more wrinkled the berries become. Any mush berries should be discarded.