How did Frodo get his Mithril Coat back?

[Runes]

Originally Posted by Galadriel55

d4rk3lf has it. The story does not elaborate on how the mithril coat passed from Shagrat to the Mouth of Sauron, but it's assumed that the orc handed it over to the authorities, and Sauron decided to give it to the Mouth to present before the Captains of the West. And Gandalf took it from the MoS.

But what is the "Mouth of Sauron"? So does that mean Gandalf entered Mordor to negotiate? Or did this happen during the battle in front of the Morannon?