Brother Fir seeks the Heartstone for Crispin's coronation. However, Fir knows the Heartstone's weight and feel. He lets Hope play with it. It did not drop out of Hope's paw. Thats how Fir discovers that the Heartstone is missing and has been replaced by a fake stone, which was presumably made by Aspen and switched by Husk.
Hope accidently finds it at the end of the book when he is giving the people on the beach shells. It is revealed that the Heartstone was thrown into basalt that was loaded onto a ship and carried away from Mistmantle, it then returns on the ship that Urchin comes home to Mistmantle on.