Final answer:
The ligament that lies between the layers of another ligament and is situated in front and below the fallopian tube is the broad ligament.
Step-by-step explanation:
The ligament that occupies space between the layers of another ligament and is located in front and below the fallopian tube is known as the broad ligament. This ligament is a fold of peritoneum that serves as a primary support for the uterus, extending from both sides of the uterus and attaching it to the pelvic wall.
The round ligament also attaches to the uterus near the uterine tubes and extends to the labia majora, but does not fit the context of the question as it does not lie between the layers of another ligament.