Is the story true about Amir al-Mu'minin Ali ibn Abi Talib restoring a severed hand of a thief by spitting on it?

A young boy's hand was broken and then set. The Prophet ﷺ came, and the boy presented his left hand to eat, so the Prophet forbade him. When he learned that it was broken, he removed the splint and wiped the boy's hand, and it healed, so he ate with his right hand. When an old man who had not yet embraced Islam witnessed the Prophet's miracle, he embraced Islam.