Cut the rabbit into pieces with a sharp knife. Cut around the joints and disjoint the pieces, this will avoid having small rabbit bones, which are very pointed, in the rillettes.
In a large cauldron, brown the rabbit pieces on each side.
Set aside in a dish, and put in its place the chopped onions (add a bit of oil if necessary), until they are lightly browned.
Put the rabbit pieces back in the cauldron, moisten with the white wine, then add the thyme, bay leaves, salt, and pepper, and 1 container of duck fat (300 g).
Bring to a boil, cover, then reduce the heat and simmer for 2 hours 30 to 3 hours.
Remove the cauldron from the heat, and let it cool for 20 minutes.
Remove the meat pieces from the cauldron, leaving the cooking juice inside.
Shred the meat, being careful not to forget small bones.
Put the two remaining containers (600 g) of duck fat in the cauldron and put it back on the heat to melt slowly.
Add the shredded rabbit meat and cook for 10 minutes, stirring constantly.
Season to taste, being careful, however, as the rillettes always seem saltier hot than cold.
Put the preparation in plastic containers, making sure the rillettes are covered with duck fat.
Let it cool completely before freezing.
The rillettes can be kept for a week in the refrigerator.