It is claimed classical scholarship claims Khilafah to be the mother of all duties (الخِلَافَةُ أُمُ الفَرَائِض) with some attributing this saying to Abu Hanifah, Shafi'i or the contemporary Mufasir Ibn Ashur.
After searching for this phrase, I could not find it in any classical text. The closest phrase I found was that mentioned by scholars like Ibn Taymiyyah:
يَجِبُ أَنْ يُعْرَفَ أَنَّ وِلَايَةَ أَمْرِ النَّاسِ مِنْ أَعْظَمِ وَاجِبَاتِ الدِّينِ؛ بَلْ لَا قِيَامَ لِلدِّينِ وَلَا لِلدُّنْيَا إلَّا بِهَا. فَإِنَّ بَنِي آدَمَ لَا تَتِمُّ مَصْلَحَتُهُمْ إلَّا بِالِاجْتِمَاعِ لِحَاجَةِ بَعْضِهِمْ إلَى بَعْضٍ
It is obligatory to know that the office in charge of commanding over the people (i.e., the Khilafah) is one of the greatest obligations of the Deen. In fact, the affairs of Deen and Duniya cannot be established except by it as the well-being of the sons of Adam is not achieved except through social life because they are dependent on each other. (Majmu al-Fatawa, Vol. 28 p. 390)
I also found a reference for a book published by a Pakistani Hizb Tahrir member, (نَفِيِد بُوت) Naveed Butt, in an article dated 11/11/2014, titled (إِقاَمَةُ الخِلَافَةِ هِيَّ أُمُ الفَرَائِض) 'The establishment of Khilafah is the mother of duties'.
The statement is attributed to Abu Hanifah, however the closest statement I found was his statement in discussing the issue of Khuruj 'Ala al-Hakim (rebellion against the ruler) where he said it is wajib if he is a fasiq and if he does not enjoy the good and forbidding the evil (ya'muru bi-lma'ruf wa yanha 'an al-Munkar). Abu Hanifah argues this activity is primarily fard and can't be established except by the establishment of the state and so it is not compared to any other fara'id (duties) in terms of importance. Al-Jasas narrates Abu Hanifah as saying:
ِوَهَذِهِ فَرِيضَةٌ لَيْسَتْ كَسَاِئرُ الفَرَائِضَ لَأَنَّ سَائِرَ الفَرَائِضَ يَقُومُ بِهَا الرَجُلُ وَحْدَهُ، وَهَذَا مَتَى أٌمِرَ بِهِ الرَجُلَ وَحَدَهُ أَشَاطَ بِدَمِهِ، وَعَرَّضَ نَفْسَهُ لِلْقَتْل
This faridah (a'muru bi-lma'ruf wa nhi 'an al-Munkar which is entitled by the state) is not compared to any other fara'id, because the rest of fara'id can be established by any man alone but if a man does this alone, he will shed his blood and exposes himself to murder ... (al-Jasas, Ahkam al-Qur'an, Vol. 2, p. 39)
The concept of khilafah being the mother of all fara'id is however correct, articulated in various forms by scholars over the centuries.
Imam Qurtubi for instance cited it as the pillar upon which all other pillars ar built:
ثُمَّ إِنَّ الصِّدِّيقَ رَضِيَ اللَّهُ عَنْهُ لَمَّا حَضَرَتْهُ الْوَفَاةُ عَهِدَ إِلَى عُمَرَ فِي الْإِمَامَةِ، وَلَمْ يقل له أحد هذا أمر غيروَاجِبٍ عَلَيْنَا وَلَا عَلَيْكَ، فَدَلَّ عَلَى وُجُوبِهَا وَأَنَّهَا رُكْنٌ مِنْ أَرْكَانِ الدِّينِ الَّذِي بِهِ قِوَامُ الْمُسْلِمِينَ
When Abu Bakr was about to die he proposed Umar to be the Imam. No one said this is not wajib on us or you. Rather this indicates its obligation as the Khilafah is the pillar upon which other pillars rest. (al-Qurtubi, al-Jami' li Ahkam al-Qur'an, 1:265)
نَصْبُ الْإمَامِ مِنْ أَتِمُّ مَصَالِحِ الْمُسْلِمِينَ وَأُعْظَمِ مقَاصِدَ الدِّينِ
Appointing an Imam is the best in meeting the interests of the Muslims and in achieving the greatest aims (maqasid) of the Deen. (Al-Iji, al-Mauaqif, Vol. 3, p. 581)
Ibn Khaldun observed:
ثُمَّ إِنَّ نَصْبَ الْإمَامِ وَاجِبٌ قَدْ عُرِفَ وُجُوبُهُ فِي الشَّرَعِ بِإِجْمَاعِ الصَّحَابَةِ وَالتَّابِعِينَ، لِأَنَّ أَصْحَابَ رَسُولِ اللهِ صَلَّى اللهُ عَلَيه وَسَلَّمَ عِنْدَ وَفَاتِهِ بَادَرُوا إِلَى بَيْعَةٍ أَبِي بِكَرٍّ رَضِيَ اللهُ عَنْه وَتَسْلِيمُ النَّظَرِ إِلَيه فِي أُمُورِهُمْ. وَكَذَا فِي كُلٌّ عصرمن بَعْدَ ذَلِكَ.
...the Sahabah agreed unanimously after the death of the Messenger (saw) on appointing the Imam and made it the most important obligations, even preferring it to the burial of the Messenger (saw) and remained committed to this great obligation in every period. (Muqadimat ibn Khaldun, p. 131)
فَكَانَ وُجُوبُ نَصْبِ الْإمَامِ مِنْ ضَرُورَِيَاتِ الشَّرَعِ الَّذِي لَا سَبِيلً إِلَى تَرْكِهِ فَاِعْلَمْ ذَلِكَ.
from the necessities of the shari'a that simply cannot be left (al-Ghazali, al-Iqtisad fi al-I'tiqad, p.128)
Al-Amidi stated it was:
فَإذاً نَصْبُ الْإمَامِ مِنْ أَهَمِّ مَصَالِحِ الْمُسْلِمِينَ وَأُعْظَمِ عَمَدِ الدِّينِ
from the greatest interests of the Muslims and greatest pillars of the deen (al-Amidi, Ghayat al-Muram, Vol. 1, pp.366-367)
Ibn Taymiyyah said it was:
يجب أن يعرف أن ولاية أمر النَّاسِ مِنْ أَعْظَمِ وَاجِبَاتِ الدِّينِ
It is important to know that one of the greatest obligations of the deen (Ibn Taymiyya, al-Siyasah al-Shar'iyyah, p.129)
Al-Haskafi observed it to be:
وَنَصْبُهُ [الإمام] أَهَمُّ الْوَاجِبَاتِ
the most important of obligations (al-Haskafi, Radd al-Muhtar, 1:548).
And Dr. Ziauddin Sardar stated:
"The Khilafah is the most important religious position and concern for all the Muslims. The Islamic Shari'ah has stipulated that the establishment of Khilafah "Caliphate" is an essential obligation of the Deen. Rather, it is the greatest obligation for the reason that the implementation of all other obligations is dependent on it". (Islam and Khilafah, p.99)
The exact term "Umm al-Fara'id" is not mentioned by any of the classical scholars, according to my research.
If the questioner means whether scholars argue for the fundamental and foundational importance of Khilafah amongst all the hierarchical fara'id in the deen, the answer would be a categoric yes.
Al-Amidi, Ghayat al-Muram
Al-Ghazali, al-Iqtisad fi al-I'tiqad
Al-Haskafi, Radd al-Muhtar
Al-Jasas, Ahkam al-Qur'an
Ibn Taymiyyah, Majmu al-Fatawa
Ibn Taymiyyah, al-Siyasah al-Shar'iyyah
Ibn Khaldun, Muqadimat ibn Khaldun
Naveed Butt, The Establishment of Khilafah is the Mother of all Duties
Shamsuddin al-Ramli, Ghayat al-Bayan
Qurtubi, al-Jami' li Ahkam al-Qur'an
Ziauddin Sardar, Islam and Khilafah
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