What is the authenticity of the hadith which mentions that the Prophet, peace and blessings be upon him, prayed Fajr while he was in a state of ritual impurity (junub), and he performed ablution for prayer (wudu'), then he bathed after the prayer because there was no time for ghusl (ritual bath)?

What has been heard is not based on শরী‘আ proof, as the consensus of the scholars is contrary to what was mentioned. According to the Hanbalis, Shafi‘is, and Hanafis, water must be used in this situation, even if it leads to praying after the time for prayer has expired. As for the Malikis, tayammum is obligatory to preserve the time of prayer. Sheikh al-Islam Ibn Taymiyyah mentioned that there are two opinions on this issue: The first, held by Abu Hanifa, the Shafi‘is, and Ahmad, enjoins seeking water even if one prays after sunrise. The second, held by Malik, enjoins praying on time with tayammum, because the time is given precedence over other obligations of prayer.