The exact moment of Pearl's transformation in Nathaniel Hawthorne'sThe Scarlet Letteroccurs in chapter XXIII, after Arthur Dimmesdale gives his final election day speech addressed to the "people of New England", and where he confesses to be the sinner upon which the scarlet letter should have been bestowed.
It all begins when, after the final disclosure of his sin, Arthur Dimmesdale asks Pearl for a kiss. The first time Dimmesdale had kissed Pearl, it was when he met Hester in the forest; a forest whose darkness was symbolic of the secrecy and sin that still permeated the relationship between he and Hester. For this reason, Pearl rejected him then, and washed his kiss off her cheek.
This time, as the narrator explains, was different. Something supernatural seems to have taken place:
Pearl kissed his lips. A spell was broken. The great scene of grief, in which the wild infant bore a part, had developed all her sympathies ... Towards her mother, too, Pearl's errand as a messenger of anguish was all fulfilled.
We know that shortly after Dimmesdale's death, comes Chillingworth's own death. As an act of perhaps guilt, or redemption, Chillingworth leaves his possessions to Pearl, of all people. As a result of that, Pearl is able to take care of her mother and the full circle of Pearl's life is complete.