I think the letter is genuine. How could it not be, if the only people who know about the plot are the ones directly involved?
Come on, guys, better than the usual vanilla rom-com, it would be a nice change if she got the money, became a proper, independent lady, and then could compete for the Prince's attentions as an equal.
Of course, that would defeat the premise of the Prince's mysterious effect on women. So I guess either his symptoms will come back with a vengeance when she's away, or the story will take a completely new direction.