This letter exists in the Jay papers as a facsimile included in a sale record.  The write up of the letter, which gives the date as November 19 is full of errors, and though the image is blurry, the month is better rendered as "Sept" -- to see the letter, look at the associated citation.  Additionally, Monroe makes mention of a previous letter from Jay sent the 24th of the month and Jay wrote to Monroe on that date (A Comprehensive Catalogue of the Correspondence and Papers of James Monroe, pg. 33).  This also appears to be the the first letter Monroe sent to Jay, which makes the November dating even less likely. The Catalogue does not record a letter from Monroe to Jay on September 19 or November 19.