Remove bone from turkey (you may want to ask the butcher to remove the bone for you). Place turkey, skin side down, between two pieces of plastic wrap. Using the flat side of a meat mallet, pound turkey lightly from the center to the edges into an even thickness. Discard plastic wrap. Sprinkle turkey evenly with the 1/2 teaspoon salt and the 1/2 teaspoon pepper.
For stuffing, remove casings from sausage, if present. In a medium bowl combine sausage, green onions, figs, and fennel seeds.
Spoon stuffing over half of the turkey; fold the other half of turkey over stuffing. Using heavy 100-percent-cotton kitchen string, tie turkey in several places. Rub skin with the oil and sprinkle evenly with the 1/4 teaspoon salt and the 1/4 teaspoon pepper.
For a charcoal grill, arrange medium-hot coals around a drip pan. Test for medium heat above pan. Place turkey on the grill rack over drip pan. Cover and grill for 1-1/2 to 2 hours or until turkey is no longer pink (170 degrees F) and center of stuffing registers 165 degrees F. (For a gas grill, preheat grill. Reduce heat to medium. Adjust for indirect cooking. Grill as directed.)
Transfer turkey to a cutting board. Cover with foil; let stand for 10 minutes before carving.