Out of the Unknown (1965) : 3x3

If, by an accident of science, it became possible for the personality to pass at the moment of death into the mind of someone still alive, then the big new problem would be into whom. To foist the wits of a rogue onto an unwilling recipient would be unjust indeed. Any government who could thus cheat death might indeed win a popular vote, but only so long as all was voluntary - mutually contracted. James Hale is a man of such a society. He has insured against death of his personality by arranging mutual "Contact" contracts with his relatives. He is already host to his late father with whose memories and prejudices he has now learned to live. He himself is a responsible parent of twins whose Contact he will arrange when they are of age.