Complete works 15 episode 6, Sophie accidentally fell into the river. When she was lifted by William, she took it out of her pocket and found that the badge had split in two. Then William saw it.

As for me, it is a letter from Owen to William in the fourth episode, which says that William is the person Sophie is waiting for. At the beginning of the fifth episode, William looked for Sophie's letter to read the I in the signature. Unfortunately, Susan tampered with the letter, but later William found Sophie's signature from Sophie's file. After seeing me, he knew that Sophie was his princess.

William moved the windmill to the bus stop as a birthday present for Sophie.