In the end, Laurence won the bid.
He bought the necklace not only because it belonged to his family, but also because he wanted to give the necklace to Noelle.
Once he confessed his feelings to Noelle, he would give this necklace to her as a token of their feelings for one another.
The only person he wanted to marry was Noelle. With him as the head of the family, she would then be the missus. Since the necklace had once belonged to a previous lady of the Longbottoms’ house, he would make it s