And the answer is …

… the Jacobson’s organ inside the mouth of an African Elephant.

This was a really tough one!

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More about the Jacobson’s organ:

The Jacobson’s organ or vomeronasal organ is an auxiliary sense of smell organ that is found in many animals. This organ is the sense organ involved in the flehmen response in mammals. The Jacobson’s organ is mainly used to detect pheromones, chemical messengers that carry information between individuals of the same species. Its presence in many animals has been widely studied and its importance for reproduction and for social behavior has been shown in many studies.

Its presence and functionality in humans is controversial, though most studies agree the organ regresses during fetal development. Elephants transfer chemo-sensory stimuli to the Jacobson’s organ in the roof of their mouths using their “fingers”, at the tips of their trunks.