The Uyghur official who introduced the Uyghur script to the Mongols was Tata-tonga. He was a Uyghur scribe captured after Genghis Khan defeated the Naimans around 1204.
Tata-tonga’s importance came from adapting the existing Old Uyghur alphabet to write the Mongolian language. The Mongols already possessed a powerful oral tradition, but a durable writing system was essential for recording laws, orders, diplomatic correspondence, tax records, and administrative information across a growing empire. Tata-tonga reportedly taught the script at the Mongol court, including to members of the ruling family.
The traditional Mongolian script was written vertically, in columns running from left to right. It remained influential for centuries and later provided the basis for the Manchu script. “Kököchü” and “Yelü Chucai” were associated with Mongol-era political or administrative life, while Subutai was a celebrated military commander; neither is the canonical answer to this question.