Heat apples, water, and cider in a large pot; let boil and lower heat. Place lid on half the pot and simmer 30 minutes or until apples are soft.
Using a food processor or blender, puree apple mixture until coarsely chopped. Spoon mixture back into pot.
Mix sweetener, lemon juice, salt, cloves, cinnamon sticks, and anise into pot and cook on low 1 hour, stirring often. Remove cinnamon sticks and star anise. Spoon mixture into an airtight container, let cool, and then place in refrigerator until chilled.