They didn't, it was built from scratch. It's likely that the only original bit might be the data plate, which would have been recovered from the firewall. Spitfires undergo what are called 'Frame Five' restorations, Frame Five being the firewall and as long as you have a data plate from Frame Five, you can call your Spitfire an original. There isn't much that is 'original' in warbird restorations of this nature, some incorporate original spars, u/c legs etc, but you can guarantee the skin work and much of the structure is built new. This is an argument that many key strokes have been expended on is just how 'original' are today's warbirds.
Regarding Hoffman props, all new Spitfire blades are made by Hoffman in Germany, ironically. Dowty (Rotol) no longer make that type of prop (obviously) and it costs a fortune to acquire drawings from them. There's a guy who owns a two-seat Spit IX in New Zealand and he has pranged it on landing twice now, so his propeller has been rebuilt three times by the same prop shop...