Hmm, this brings up an interesting question: is it possible to eliminate or poison the data you leave behind in order to render it impossible for people to accurately simulate you after death? I'd be very interested in that.
Sadly Audrey Hepburn couldn't sing and was always dubbed (Just you Wait being an exception, and hardly singing). So it seems she has achieved something in death she never did in life.
Your integrity is intrinsically linked with your body and your function in society.
Integrity after death implies something you have identified with is preserved when your body is gone.