SPOILERS:
Remus seeks out Harry, Ron and Hermione at Grimmauld Place and offers to accompany them on their quest, but Harry refuses. He recognizes that Lupin is seeking escape from complications in his personal life and Harry argues that he needs to be with Tonks.
Kreacher returns with Mundungus, who reveals that Umbridge took Slytherin's Locket from him as a bribe for excusing his crimes like selling magical artefacts without a license.