Inspired by this answer and the comments following.
If the first day of Yom Tov (not Rosh Hashana) is Shabbos, an Israeli will make a normal havdalah המבדיל בין קדש לחול, while someone from outside Israel will make havdalah during kiddush המבדיל בין קדש לקדש.
Can either of them be yotzei by listening to the other? Or do they still have to make their own correct havdalah?
I'm interested in both the lechatchila and bedieved answers.