The Billionaire Farmhand I Picked Up

A billionaire CEO travels to a rural area, suffers an accident, loses his memory, and is picked up by a rural female protagonist. Her sister lies to the man, claiming they are in a romantic relationship. The man believes it, but the female protagonist exposes her sister's lie. Her snobbish parents force her to pay living expenses. With the man staying, she faces extra costs she cannot afford. The sister then notices the man looks exactly like the billionaire CEO on television.