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i think the sios didn't have enough influence when the prince was first brought back or maybe even with the duke droit they still wouldn't be able to fight of the emperor's army together with the other duke's [father of the female lead]. Or maybe they just thought it would be easier to pass him as the ML's child since when he dated Lisena she had him wrapped around his finger. It'd be a lot less trouble, less bloodshed and they were also trying to make Lisena empress. The thing is she miscalculated and the prince is now in a position to be easily killed by the ML if he wanted to, if he ever were to learn the truth about the boy.
Technically isn't the son of the real dead crown prince the strongest contender for the throne??? Doesn't his authority overtake the current emperor who took the throne from a coupe