Heat the pan (fat free). Once hot, place the pieces of meat on the skin side. The skin of the duck will start to melt. Once the skin is golden brown, remove the pieces of duck and set them aside. Remove most of the fat from the pan (but keep a little bit of it).
In the pan with the rest of the duck fat, add the sliced onions and cook them for 1 to 2 min. Add the garlic. Deglaze with the port and white wine. Let simmer for about 5 minutes.
Add the olives, the mushrooms and the meat. Season with salt and pepper to taste.
If using a pressure cooker, close and cook for 25 to 30 minutes from the rotation of the valve. If you use a classic pan, the cooking time will be longer.