Sir Edward gave Suffer to Emily-with-a-y during her stay in the Asylum for Wayward Victorian Girls. It was a gift from the League of Plague Rats for Emily-with-a-y because she (and other members of the Striped Stocking Society) had buried a rat that they had found dead in a pot of soup. Suffer had originally belonged to a girl who was a great supporter of the League of Plague Rats but she had been bled dry by leeches several years ago. So, Sir Edward gave Emily-with-a-y Suffer (the former girl's only belonging) as a gift of thanks.
I hope that all makes sense since you haven't read the book