What finally laid Liesel's brother to rest?

Liesel's brother dies on the train to the Huberman's home. She steal a book during his burial to remind her of him. Only later does she learn to read the book.

I think the word 'finally' is the key operative in the question of laying Liesel's brother to rest. Perhaps Liesel's adoptive mother--Mama--is instrumental is resolving Liesel's on-going grief of having lost her brother. Losing loved ones is central to Liesel's confusion with her place in life. Death of her brother and the subsequent loss od her mother wreak havoc in the heroine's early life journey. Shortly thereafter, she is shuffled off to live with foster parents, total strangers in her world of recurring separation.

Mama's sudden reversal as a strict disciplinarian, a 'witch' by her own words, goes a long way in assuaging Liesel's torment when the latter unexpectedly interrupts Liesel's classroom to inform her that Max was 'awaken' from his delirium and gives Lieseal the picture of her little brother that Max had kept in his book.

A second 'final' step occurs when Liesel begins to relate a story in the darkened bomb shelter, thereby allaying the feelings of fear from children and adults alike. Her recitation of the tale from H.G. Wells' "The Invisible Man" tells others to fear not, for they are not alone in darkness . . . they are merely separated momentarily like the darkness the darkness between the myriads of stars Max experiences outside during a similar bombing raid. Separation, like darkness, is only temporary . . . and thus, she has come full circle in the understanding that the bonds of love and hope with those we love is and can never completely severed.