[The ruling on praying Ẓuhr behind one praying ʿAṣr (and vice-versa)]

Answer (and Allah grants success): The scholars have differed on this; the school’s position is that it is not valid. Several points may support the school’s view:
1. From calling one of them an imām and the other a follower (muʾtamm) there is an implication of agreement in intention, aim, and the same obligatory prayer, along with outward following. If this agreement is absent, neither is an imām nor the other a follower—this is what the wording of “imām” and “follower” requires outwardly.
From this it follows that one who fights alongside the Prophet—may Allah bless him and his family and grant them peace—out of tribal zealotry is not counted as following him nor as truly imitating him.
2. Allah, Exalted, said regarding the Prophet—may Allah bless him and his family and grant them peace: “Follow him that you may be guided.” [al-Aʿrāf:158] The command to follow in this verse is to be understood as including the intention, because guidance is not attained without it.
Moreover, the command to follow is unrestricted, encompassing both outward acts and inward states.
If it be said: what you have mentioned is specific to the Prophet—may Allah bless him and his family and grant them peace—and not to the imām of a prayer,
We say: the verse concerns the Prophet (may Allah bless him and his family and grant them peace), but it is general regarding following him in the imamate of prayer and otherwise. If following the Prophet—may Allah bless him and his family and grant them peace—in the intention of prayer is obligatory upon those praying behind him, then it is likewise obligatory upon those praying behind others and there is no doubt about this.
3. Praying Ẓuhr behind one praying ʿAṣr (or vice-versa) contradicts what is well-known from the Sunnah of the Prophet—may Allah bless him and his family and grant them peace—and the Muslims after him. The best guidance is the guidance of Muḥammad—may Allah bless him and his family and grant them peace—and the worst of matters are innovations.
4. Precaution accords with what the scholars of the school have mentioned.
Those who disagreed cite evidences for validity, such as the Prophet’s—may Allah bless him and his family and grant them peace—instruction regarding emirs who delay the prayer (to its end or beyond), in which he said: “Let your prayer with them be supererogatory”; and the ḥadīth of the man who had prayed at home and then came to the Prophet’s mosque, where the Prophet—may Allah bless him and his family and grant them peace—ordered him to pray with the Muslims even though he had already prayed; and another ḥadīth in which a man came to the mosque after the Prophet (may Allah bless him and his family and grant them peace) and the Muslims had prayed, and he said (in meaning): “Who will give charity to this man and pray with him?”
Source : Min Thimār al-ʿIlm wa al-Ḥikmah vol.1