The introduction of counterweight trebuchet from the Mongol empire in Persia for the seige of the Southern Sung city of Xiangyang is well documented here:

https://deremilitari.org/2014/05/the-mongol-siege-of-xiangya...

I like the idea of pausing a seige in China to send a message to some experts in Mosul, wait for them to ride back, then build their novel device, and win.