によって Me

ok I idn't know at first who exactly told them または how did they know about it .I thought that may be they just wanted to make sure.but, I was wacthing the final episode "again" the other 日 , I noticed that when Ben told Jack all of あなた have to go back Jack told him "Kate is not even talking to me" . Ben told him that he can take care of that .so I remembered the sneak peak I saw .I started thinking is it possiable that he told them about Kate , so she agrees and go back with them .And I thought こんにちは it's Ben he can do everything .I started to look for other explnation ,like if Claire's mother told them,but how did she know that he's not Kate's baby beside when Claire was pregnent her mother was in a comma which means she doesn't even know that her daughter was pregnent . But I also thought about Jack telling them for the same reason why Benwould tell them .
It's the only explnation I have if あなた have an other theory please tell me .
Happy new 年 everybody