Does jihad al-nafs (struggle against the self) fall under jihad in the path of Allah?

Question:
Is jihad in the path of Allah a lesser jihad, as indicated by the meaning of the weak hadith mentioned, even though no one can fight in the path of Allah except one who has truly struggled against his own self and compelled it, even to the point where he wishes to surrender in the path of Allah?

Answer:
The jihad in the greater sense is the greatest jihad, as you mentioned; it is the greatest jihad. For this reason, the scholars have rejected the notion that the jihad in the greater sense implies that the jihad in the path of Allah is the lesser jihad, and this is an error. This is because sacrificing one’s souls, sacrificing one’s wealth, fighting the enemies, calling them to Islam, and bringing them out of darkness is a tremendous matter beyond what people imagine. Therefore, the jihad in the path of Allah, which involves sacrificing souls and wealth, leaving one’s lands, and parting with one’s homelands, children, and women—this jihad is the greatest jihad. Then people return from it to a greater jihad: the jihad of the self against the sins and failures that befall it, and against the dangers and deficiencies it faces. Thus, he struggles against it for the sake of Allah, which may be required. There is no doubt that the greatest jihad is what is achieved in the greater jihad by struggling against the self until it is upright in anything other than Allah, until it is satisfied with the jihad in the path of Allah, until it offers the self for the sake of wealth. This is the affair of the believer: he struggles against his self and is patient in the jihad against the disbelievers, knowing the great good in that.
And it is established from the Messenger of Allah (peace and blessings be upon him), as narrated by al-Bukhari and others, that he said: “No one dies with good in the sight of Allah who wishes to return to the life of this world, except the martyr in the path of Allah. The martyr wishes to return to this world to be killed ten times over, because of what he sees of martyrdom in the path of Allah the Exalted and Majestic. And the Prophet will say: ‘I wished to be killed at the gate of the great [battle], then be killed, then be killed, then be killed.’”