Wow the father really is an idiot, if he knew his son was sick because he was deceived then he could've found Natsumi with private investigators and 1. If she was honest, amend things with his son and her or 2. Bribe her into giving a healing story to him so he can move on.
Now? Well what idiot rich dad let's just any thot marry his son. High class rich heirs need wives of quality otherwise the family ship will sink. If he's betrayed a second time, suicide is likely so father is a dumbass for not screening them intensely and being rigid about ensuring they are pure of heart and not in it for money.
Ugh. Also, mc could've taken letter to his dad and asked him to hire private investigators to figure out which girl is Natsumi by promising to marry her and do whatever his dad wants, easy peezy.