Stir the stock, oil, garlic, jerk seasoning, vinegar, salt and black pepper in a shallow, nonmetallic dish or gallon-size resealable plastic bag. Add the beef and turn to coat. Cover the dish or seal the bag and refrigerate for 8 hours, turning the beef over a few times during the marinating time.
Lightly oil the grill rack and heat the grill to medium. Remove the beef from the marinade and pour the marinade into a 1-quart saucepan.
Grill the beef for 25 minutes for medium-rare or until desired doneness, turning the beef over once halfway through the grilling time.
Heat the marinade over medium-high heat to a boil. Reduce the heat to low. Cook for 10 minutes. Stir in the lemon juice and cilantro.  Serve with the beef.