A traveler who did not pray Maghrib until the time of 'Isha' passed by the people of a village while they were praying 'Isha'

The questioner : Praise be to Allah, Lord of the worlds, and may peace and blessings be upon our Prophet Muhammad, and upon his family and all his Companions.
The questioner says: A traveler did not pray Maghrib until the time for 'Isha' had arrived, so he passed by the people of a village who were praying 'Isha', and another man from the village prayed with them intending Maghrib, thinking that they were praying Maghrib. What is the situation of each of these two men? Please give us a ruling on this, mentioning the evidence, and may Allah reward you with good.

The Shaykh : Praise be to Allah, and may peace and blessings be upon the Messenger of Allah, his family, his Companions, and whoever supports him.
The truth is that we do not have a text regarding this specific issue about which the question was asked; rather, it is derived through a degree of deduction and independent legal reasoning. We say that it is established in the Sunnah that a difference in intention between the intention of the follower and the intention of the imam does not affect the validity of the prayer or the validity of following. For example, there is the prayer of Mu'adh ibn Jabal of the last 'Isha' behind the Prophet (peace and blessings be upon him), and then his prayer of it with his people. As stated in Sahih al-Bukhari, it would be a voluntary prayer for him and an obligatory prayer for those behind him. Also, there are some authentic hadiths regarding one of the ways the Prophet (peace and blessings be upon him) prayed the prayer of fear with his Companions. Among these is that he would pray two rak'ahs with the first group, then say the closing salam with them. These people would then move to the ranks of the other group so that they could come and pray behind the Prophet (peace and blessings be upon him) for two rak'ahs. Naturally, the first two rak'ahs would be the obligatory prayer for the Messenger (peace be upon him), and the last two rak'ahs with the other group would be a voluntary prayer.
And perhaps there are other examples that I do not recall at this moment. Also, we must mention here the incident of that Bedouin who was working in the open fields during the day and would come in the evening to pray behind Mu'adh (may Allah be pleased with him). One day, when he followed him in the last 'Isha' prayer and heard him begin Surat al-Baqarah, he thought, or it was suggested to him, that this recitation would be very long, very long indeed for him. So he cut off the prayer behind Mu'adh and prayed alone. When we look at these texts, we can say that the prayer of this traveler or that resident who followed the imam while he was praying 'Isha', and each of them assumed that he was praying Maghrib, but it became clear to him that he was actually praying 'Isha', is as follows: In this case, if he catches the imam in the first rak'ah, then when the imam stands up for the fourth rak'ah, each of them should intend to separate and cut off following the imam, so that he sits for the final tashahhud at the end of the third rak'ah for him. He then says the salam, then stands up and follows the imam for whatever of the 'Isha' prayer he catches up on.
This is what appears to me as the answer to this question.
Yes.