Step 1: The nasolacrimal duct carries tears from the lacrimal sac down into the nasal cavity. It opens into the inferior meatus of the nose, beneath the inferior turbinate.
Step 2: At this lower opening there is a mucosal fold or flap that acts as a valve, called the valve of Hasner. It prevents air and nasal secretions from being forced back up into the lacrimal system. Hence Hasner's valve is the correct answer.
Step 3: The Heister valve, also called the spiral valve, is found in the cystic duct of the biliary tree, not in the lacrimal apparatus, so those options are incorrect.