What muscle is the prime mover for a seated lateral dumbbell raise to shoulder level with elbows slightly flexed?

The biceps brachii acts on the elbow joint as a flexor and supinator and on the shoulder as a weak flexor; it has no role as a prime mover for shoulder abduction.

The posterior deltoid is the prime mover for shoulder extension and horizontal abduction (as in a rear deltoid fly), not frontal-plane abduction.

The anterior deltoid is the prime mover for shoulder flexion (front raises) and assists with internal rotation, not lateral abduction in the frontal plane.

The middle (lateral) deltoid originates on the lateral border of the acromion and inserts on the deltoid tuberosity of the humerus, making shoulder abduction in the frontal plane its primary function. Raising the arm laterally to shoulder height (approximately 90 degrees of abduction) maximally recruits the middle deltoid, and slightly flexed elbows reduce unwanted contribution from the supraspinatus and anterior deltoid.