Suppose that oneself consciousness is being transported to another body, would it be correct to say that you (the consciousness) had a new body, or that body had a new consciousness (you)? Could you regard yourself as the same person, with a different body? Perhaps you could.

Suppose the body were of the opposite sex, could you regard yourself as the same person?

Suppose the consciousness is being transported to an animal, could you regard yourself as the same person? Much of what makes you, your personality, capabilities and so forth, is tied to chemical and physical conditions of the new body (animal). And what if your memory were wiped out during the transfer? Does it then make any sense at all to regard the new animal as you?

These questions arise when one speculates about "duplication of the self" regardless of any forms. And this is one of the centric philosophies in Hinduism and Buddhism.

If you are interested, kindly refers to “consciousness” topic for additional discussion.

Extract from wiki, in a 2007 interview with Time magazine, Cameron addressed the meaning of the film's title, answering the question "What is an avatar, anyway?" Cameron stated, "It's an incarnation of one of the Hindu gods taking a flesh form."
He said that "in this film what that means is that the human technology in the future is capable of injecting a human's intelligence into a remotely located body, a biological body". Cameron stated, "It's not an avatar in the sense of just existing as ones and zeroes in cyberspace. It's actually a physical body."