Authenticity of a letter Hulagu Khan purportedly sent to the Mamluks?

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Amitai-Preiss, Reuven, Mongols and Mamluks: The Mamluk-Ilkhanid War, 1260-1281 (Cambridge Studies in Islamic Civilization), Cambridge: Cambridge UP, 1995, p. 36, states that the content of the letter is cited in the work of Egyptian Historian Ibn al-Furāt (d. 1405) as well as al-Maqrizi (d. 1442) (note 64).

Note 64 also mentions that famous Mongol-Ilkhanate historian, Rashīd al-Dīn Faḍlullāh Hamadānī (d. 1318) cites a shortened version of the letter in Persian in his Jāmiʿ al-Tawārīkh ("Compendium of Chronicles").

These three Egyptian and Persian sources seem to share the basic outline.