Hadith: I witnessed the Messenger of Allah (may Allah's peace and blessings be upon him) give a quarter (of the war spoils) as extra booty on the way out to a battle and a third on the way back

عن حبيب بن مسلمة الفِهْري قال: «شَهِدت النبيَّ صلى الله عليه وسلم نَفَّلَ الرُّبْعَ في البَدْأَةِ، والثُّلُثَ في الرَّجْعَة».
[صحيح] - [رواه أبو داود وأحمد]

Habīb ibn Maslamah al-Fihri reported: I witnessed the Messenger of Allah (may Allah's peace and blessings be upon him) give a quarter (of the war spoils) as extra booty on the way out to a battle and a third on the way back.
Sahih/Authentic. - [Abu Dawood]

Explanation

It is permissible, according to this Hadīth, to assign extra spoils to an army detachment, in addition to the shares they receive, in appreciation of their effort in Jihad. If the detachment makes an incursion at the beginning of the journey to Jihad, they shall be given a quarter of the booty they gain. If they make an incursion after the return of the Jihad fighters, they shall be given a third of the booty they gain and they share the rest of the booty (three-quarters or two-thirds) with the rest of the army. They receive more after Jihad than before, because the soldiers are weak then and the detachment has less support than if they make an incursion before Jihad is launched. Also, they deserve more because they are fighting at a time when they have an intense desire to going home and see their families.