Bring large saucepan with 3 quarts salted water to boil. Add duck, reduce heat and cover to simmer for 2 to 2 1/2 hours until tender. Remove duck and strip flesh from carcass and dry with cloth. Strain cooking liquid and let cool. Once cooled, skim fat and reserve.
Heat oil in frying pan and add duck pieces, frying 15 minutes until crisp brown on all sides. Return duck to large saucepan, add 1 3/4 cups cooking liquid, 1 cup pineapple pieces, green pepper and ginger. Cover and simmer another 15 minutes. Remove duck and rest on heated serving dish to keep warm.
Skim any fat from surface of cooking liquid and bring to a boil. Separately combine pineapple juice, soy sauce, pepper and arrowroot, mixing well. Add this to cooking liquid and stir until it thickens and clears. Pour sauce over duck.