I am intrigued by the use of the pronoun here. Horatio is clearly referring to the king even though the ambassador has not specifically mentioned him – but “his mouth” seems like a kind of casual reference to a king – even a dead one.
A more formal way to say it would seem to be not from the king’s mouth. But it’s not that. It leaves room for misinterpreting. “His mouth” could, for a moment, be any of the three dead men. Any of them. The next line tells us which mouth Horatio is referring to but even then it might not be clarified for the ambassador and Fortinbras. We know because we know – but the newly arrived characters might still be in the dark. They won’t get the facts from his mouth.