Interesting Shailah from Sukkos

I haven't had a chance to catch up on my bloggiong since Sukkos so here is an interesting Sukkos question.

Someone made a mistake on Yom Tov and instead of davening Yom Tov mussaf they davened Yom Tov shachris/mincha (shachris and mincha is the same tefilla) . They then remembered and davened mussaf. It is now time for mincha.The question is that when this person mistakenly davened Yom Tov shachris/mincha instead of musaf, it was after zman mincha, therefore maybe this tefilla should count for mincha. Do they have to daven mincha again?

The Ishei Yisroel brings this halacha down. Interestingly, it is a teshuva in the Igros Moshe. R' Moshe paskens that one does not need kavanna for which tefilla you are davening, therefore the person would not need to daven mincha again. Rav Moshe bases this on a MG"A that says if you daven Shabbos musaf instead of shachris you don't need to repeat musaf. Even though when you davened mussaf your kavanna was for shachris, kavanna is not m'akeiv.
The Ishei Yisroel does mention that the Shoeil U'Meishiv argues on this point.