Is the story of the greetings exchanged between the Prophet, Gabriel, and the angels at the Lote Tree of the Utmost Boundary authentic, the one taught to children to help them memorize the Tashahhud?

This story has no origin or basis in the authentic books of Sunnah. The story of the Mi'raj (Ascension) is firmly established with its details in Sahih al-Bukhari, Sahih Muslim, and other collections, and it contains nothing about the occasion for mentioning the known tashahhud in prayer. Indeed, the two Shaykhs (Bukhari and Muslim) narrated from Abdullah ibn Mas'ud, may Allah be pleased with him, that the Prophet, may Allah's prayers and peace be upon him, taught the Companions the known tashahhud. What has been mentioned in some books of tafsir (exegesis), commentaries on the Sunnah, or books of fiqh (jurisprudence) and Sufism regarding this story is an unauthenticated, unreferenced mention, and it is impermissible to attribute it to the Prophet, may Allah's prayers and peace be upon him, due to the absence of any authentic origin for it.