Legal Question in Real Estate Law in California

First, there is a section of the Code of Civil Procedure that authorizes a legal action (suit) for relief of someone who has, by misunderstanding of law or fact, made improvements upon land owned by another in a good-faith belief that he had the right tp do so. See CCP sections 871.1 to 871.7. However, this law probably doesn't apply to your father's situation. See CCP section 871.6, which says the good-faith improver law doesn't apply to cases of encroachment by an adjoining landowner.

More likely, your father will have to rely upon either (a) a voluntary lot-line adjustment, which would probably be subject to local minimum lot-size ordinances, and would require the neighbor's cooperation and perhaps the payment of some consideration, or (b) a suit to quiet titleto a prescriptive easement in the area in the neighbor's ownership that is occupied by the house.

A voluntary settlement is somewhat to be preferred, if the city or county will allow the lot-line adjustment, even if your father has to pay the fair market value for the land (unless it is a lot of land or the value is extremely high). It would preserve better relations between the neighbors and is more certain than a suit for a prescriptive easement. However, a lawyer who has access to all the facts can give you a better overall prognosis.