That isn't the story I'm thinking about. In the story the reconstructed person is in a real body, a real mind - he's been mapped onto a living person's brain. Since his style of music is no longer popular, he produces a new symphony in the style of the day, despite knowing it's still a rehash of his previous work. At the end of the performance, everyone applauds... but they're actually applauding the neuroscientists for their work, not the composer for his, and in the end he gets 'erased' so that the test subject can have his mind back. It might be a story from the 50s, since I seem to remember reading it in an anthology of such.