The Shroud of Turin and the Shawl of St. Veronica are two separate artifacts.

The Shawl of Veronica, as my understanding goes, disappeared from Rome somewhere in the 1500's or as late as 1600. There is a belief that a shawl found about a dozen + years ago, at a Capuchin Friary in the town of Manoppello, is the shawl, but that is still under investigation. Of course, there is also speculation that St. Veronica did not actually exist and that Veronica is a bastardization of vera icon, meaning true image. Thus, the image on the shawl was actually made, but over the years the story was diluted to the point that vera icon became Veronica and the word was then identified with the woman who gave the shawl to Jesus. Veronica is not a name that fits either the place or time.

The Shroud of Turin was the burial cloth for Jesus and would be far too large to have ever been a shawl.