Horner's syndrome is a group of symptoms that include sinking in of the eye with drooping eyelid and an absence of sweating. Horner's syndrome and neck or shoulder pain can be related when they are both caused by pressure on the nerves to those structures.
A form of lung cancer called Pancoast tumor is the most common cause of neck or shoulder pain with Horner's syndrome. In this type of cancer, tumors fill the upper lung lobes. When cancer cells leave the lung and extend further up, the nerves to the arms, neck, and face can be affected.
These conditions can be very serious. You may want to make an appointment to talk with your father-in-law's doctor and get the full details.