The trap was set.
As planned, William made contact with Elisha and the conversation between them was good enough to get her communication number.
After returning to the academy, he kept in touch with her through this. This part was important because she had to fall in love with him. If not, he won't get her and his great-grandma might not get the revenge that she sought.
This was something he wouldn't let happen.
Though this plan was supposed to cause damage to the two families, for him the girl was more important. Even if the part to cause tensions between Frostwolf and Siren's family fails, he doesn't care. What he cared about was whether he could get Elisha or not.
He loves his great-grandma but this is not her life or era. It is his life and the final decisions have to be made upon what he desires, not what others desire.
So he put in the effort to not only impress Elisha but also her parents.
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Your gift is the motivation for my creation. Give me more motivation!
Creation is hard, cheer me up!