What organ lies on the outer wall of the testes within the scrotum?

The answer is the epididymis. It is a contracted, tightly-coiled tube linking back of the testicles to the deferent duct (vas deferens). The epididymis contains three parts and these are the head, body, and tail. The head of the epididymis is positioned on larger pole of testis. It stocks sperm for maturation.