Who won when the mongols invaded the forbidden city?

The Mongols never successfully invaded the Forbidden City, as it did not exist at the time of their conquests. The Forbidden City was built later, beginning in 1406, during the Ming Dynasty. The Mongol Empire, under Genghis Khan and his successors, did conquer large parts of China, but the Forbidden City itself was established as a palace complex after the Mongol Yuan Dynasty was overthrown by the Ming.