Generally speaking, standard category licenced aircrt have an indentitiy as soon as the manufacturer assigns it one. This usually happens during assemblyat the factory and stays with the aircraft until it no longer officially exists. In the case of restored aircraft, the paperwork's existance is often enough to resurrect an aircraft that may no longer exists physically, and have it officially recognized as that aircraft Another way to go might be if the just the data plate, installed at the factory, was still extant.
In the case of MANY WWII aircraft now flying, some wrecks have become others. It's quite a game. But if one can pull it off? Why not?