Using a large colander, wash the cranberries with warm water. Then, berry by berry, sort to remove any stems and soft, broken or discolored cranberries.
Place the good berries in a large pot over medium heat. Add the li hing mui powder, orange zest and juice, lemon zest and juice, sugar, salt, and star anise. Cook to just before a boil, then reduce heat to low; continue to simmer for 20 minutes.
Place in container to cool; enjoy with turkey and all the trimmings!