... with no high technology required!
Step 1: Write extensive memoirs, and have servants constantly follow you around, recording every detail of your life, in painting, story, and song.
Step 2: Drink some hemlock to kill your present body.
Step 3A: Have your servants find a newborn baby. Your servants will be experts in hypnosis, in the induction of "false" memories, and in psychological training. They will induce in the child, as she grows, memories from your past -- not false memories, but veridical, accurate memories! Memories at least as accurate and complete as other people's normal memories of three or ten years ago. With proper suggestion, the growing child will experience the memories from the first-person perspective and think of them as her own.
Step 3B (simultaneous with 3A): Surround the child with institutions designed to convince her -- I mean you -- that she/you really is just the continuation of you in a new body. She will look on all of her induced memories as memories of the old days from her previous body. She will share your name, "remember" your friends and attitudes as her own, be personally proud of your past accomplishments and personally embarrassed by your past failures, identify with your old goals, projects, debts, and obligations. With some luck and good psychological training, the child will grow into an adult who shares the values and attitudes of your old self -- perhaps about as much as normal people retain their values and attitudes over the course of a decade or two.
If she and all of society then say that she really is the re-embodiment of you -- that is, a continuation of the same person over time (only in a new body), as much as your 40-year-old self is normally thought to be a continuation of your 20-year-old self -- would she and all her society be factually, philosophically, metaphysically mistaken? If she isn't really a metaphysically legitimate continuer of you, why not? What would be missing, exactly?
You might say they aren't real memories, because they're the memories of a different person -- but to say that is just to beg the question, assuming the falsity of the very view in dispute.
You might say that personal identity requires strict continuity of body, which she doesn't have with you. But that's to move away from psychological criteria for personal identity, which many people find attractive in hypothetical upload cases, brain transplant cases, and teleporter cases.
This is the topic of my latest science fiction story, "The Dauphin's Metaphysics", now out in the latest issue of Unlikely Story.