To what extent is the emendation by Ibn al-Athir in his book Jami' accurate concerning the wording of al-Humaidi’s book al-Jam‘ bayn al-Sahihayn, and did Muhammad ibn Suleiman al-Maghribi in his book Jam‘ al-Fawa’id emendate what Ibn al-Athir missed?

Ibn al-Athir, in his book, relied on what al-Humaydi had compiled from the Two Sahihs. However, he traced the additions from all the "Umm al-Hukm" (mother books) to verify the wordings of Bukhari and Muslim, and he omitted what al-Humaydi had added from other sources. This is confirmed by al-San'ani and others, because Ibn al-Athir did not transmit al-Humaydi's book verbatim, but rather relied on it only for what pertained to the Two Sahihs. Nevertheless, al-Humaydi was not free from oversight and error, and Ibn al-Athir followed him in some of these instances. As for the book "Jam' al-Fawa'id" (Collection of Benefits), it did not add anything to its original source, but rather abbreviated some of the hadiths.