Thaw shrimp, if frozen. Peel and devein shrimp. In a medium saucepan bring 4 cups water to boiling. Add shrimp. Simmer, uncovered, for 1 to 3 minutes or until shrimp turn pink, stirring occasionally. Rinse under cold running water; drain. Set aside.
In a heavy plastic bag set in a medium bowl combine garlic, lime peel, lime juice, olive oil, onion, Anaheim pepper, cilantro or parsley, sugar, salt, and pepper; mix well. Place cooked shrimp in the bag; seal bag. Turn bag to coat shrimp with marinade mixture. Marinate in the refrigerator for 2 to 3 hours, turning the bag occasionally.
To serve, drain the shrimp, discarding the marinade. If desired, line a large platter with lettuce leaves and arrange papaya or mango slices around outer edge. Place shrimp in center of platter. Makes 6 servings.