This point is made by the authors of the Cornell University website "Mozart and the keyboard culture of his time", which also offers digital images of the letters in question. See "Tell-Tale Letters".
The Cornell University website "Mozart and the keyboard culture of his time" offers an image of the original published version of the letter, as well as one of the salient reasons why it is considered fraudulent: it has Mozart saying "the letter I wrote to my father-in-law, to request the hand of my present wife"; Constanze Mozart's father Fridolin Weber died before Mozart ever began courting her. See "A Forged Letter".