It's a very interesting idea. The molecular ID suggested by Lawfire sounds superb. I have a couple of suggestions. Why not call it a brain imprint - so the brain actually has unique electrical signals that matches the one they had in their past life. Secondly, I don't know if they should be taken away when they are children / babies. The idea is to wait for them to gain some semblance of understanding - regarding their crime, and then arrest them. Thirdly, it's re-incarnation. Your story would therefore have to be set several years into the future of the future. That one part, I think, could become complex. Otheriwse, it sounds fine.
Nice idea, indeed. I remember having seen a story where the offspring just inherited the sentence..... So father died? Son/daughter took his place. Maybe a little less complicated.
