There are several exemple of aircraft being rebuild, even after this kind of crash. For administrative reason, it's possible to rebuild a destroyed aircraft because the money has been taken on an other budget, or chapter.
In the french army an aircraft may be moved from a unit to an other losing its regiment's registration. AD is dedicated to Compiegne. So the ADJ in green could be different from the sand camo ADJ s/n 1403 of 2004.