Is the apartment, whose price was paid by the father and registered in the mother's name with the intention of gifting it to the son, considered a complete gift, and is there any sin upon the son for taking it?

A gift is not completed until the donee takes possession of the gifted item and is able to dispose of it. If someone claims a gift was made to him concerning something owned by his father, he must present evidence for that to the Sharia (definition) court. An unjust gift is revoked even after the death of the donor, according to many jurists.