How did Frodo get his Mithril Coat back?

[Runes]

In Return of the King, at the end when Frodo wakes up, Gandalf hands Frodo his mithril coat back, and Sam's sword.

However, the coat was taken by Shagrat, that ork at the Tower of Cirith Ungol. There was also a quote in the book that as Sam saw the ork escaping, he didn't know how much it would cost him, or something. Anyway, how did the coat come to Gandalf from here?

When journeying through the plains of Gorgoroth to Mt. Doom, Sam suggests they dump all the extra items they were carrying so as to lessen the weight. And they throw away everything, but its noted that Sam kept Sting. So they must've thrown Sam's original sword away (and actually, the orcs must have taken the sword away at Cirith Ungol, because Sam brings Frodo an orc sword to carry through Mordor.)

So my question is: how come Gandalf finds Sam's sword and the Mithril Coat? Its been bothering me ever since I reread the book this past week.