Combine all of the mojo ingredients in a large bowl and whisk well.
Score the skin with a sharp knife and rub the pig inside and out with 3/4 of the mojo marinade. Reserve the remaining mojo to pour over the meat after it has been carved.
Cook the whole pig in the Caja China according to manufacturer's instructions.
Preheat the oven to 325 degrees F.
Score the skin of the pork shoulder. Put it into a large bowl or baking dish and pour in 3/4 of the marinade, making sure to coat the entire piece of pork. Cover and refrigerate for at least 30 minutes or up to 2 hours.
Put the pork shoulder, skin side up, in a roasting pan fitted with a rack, Cover with foil and roast in the oven for 3 hours. After 3 hours remove the foil, turn the heat up to 425 degrees F and roast until the skin is brown and crispy, about 30 to 45 minutes. Make sure to check every 5 or 10 minutes to make sure the skin does not burn. Remove from oven to a cutting board and let rest for 10 minutes before carving. Carve the meat and arrange it on a serving platter. Pour the reserved marinade over the carved meat just before serving.