**Core Concept**
The cremasteric reflex is a physiological response in which the contraction of the cremaster muscle results in elevation of the testicle on the affected side. This reflex is significant in clinical practice, particularly for diagnosing abdominal pathology. The efferent limb of the cremasteric reflex involves the neural pathway that controls the contraction of the cremaster muscle.

**Why the Correct Answer is Right**
The efferent limb of the cremasteric reflex is provided by the genital branch of the genitofemoral nerve. This nerve originates from the lumbar plexus (L1-L2) and divides into two branches: the genital branch and the femoral branch. The genital branch innervates the cremaster muscle, which is responsible for the elevation of the testicle during the cremasteric reflex. The contraction of the cremaster muscle is mediated by the release of acetylcholine from the motor terminals of the genital branch of the genitofemoral nerve, leading to muscle contraction.

**Why Each Wrong Option is Incorrect**
**Option A:** The femoral branch of the genitofemoral nerve primarily supplies the skin of the anterior thigh and the femoral muscle, but it is not involved in the cremasteric reflex.

**Option C:** The ilioinguinal nerve provides sensory innervation to the skin of the groin and the root of the penis, but it is not responsible for the efferent limb of the cremasteric reflex.

**Option D:** The pudendal nerve primarily supplies the external genitalia, including the skin of the penis and the scrotum, but it is not involved in the cremasteric reflex.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the cremasteric reflex is a valuable clinical tool for diagnosing abdominal pathology, particularly in infants and children. The absence of the cremasteric reflex, known as cremasteric inhibition, can indicate a range of conditions, including testicular torsion or abdominal trauma.

**✓ Correct Answer: B. Genital branch of the genitofemoral nerve**