Groups claiming to be the 'true successor' to the Galactic Empire have arisen time and again. Much like countless empires have made the claim of being the successor to Rome - e.g. the Holy Roman Empire and the Byzantine (which hilariously still insisted on being the Roman Empire when it controlled barely more than Constantinople!).
Survival of the fittest and struggle will decide over whether the Remnant's or the Empire of the Hand's claim is more 'valid'. I guess both fighting it out, if it comes to it, should be fun. In the game of thrones, the only 'right' is what your power allows you to enforce.