Mind "Sculpture"=Revive The Dead?

I always remember reading a Sci-Fi story, the plot of which was the invention of a technique called “Mind Sculpture”.By means of this a living person would assume the identity/psyche of a long-dead person from the past. In the story, it worked-a volunteer became a long-dead musical composer. The downside was-the composer didn’t WANT to go back being dead again!
My question: suppose you were able to story every detail in a person’s brain (on a hard drive). Could you download this to another brain, and recreate a person?