Martyrdom does not expiate rights owed to other people; it only expiate rights owed to Allah, may He be exalted
Question

How do we reconcile between these two hadiths:
1. The Book on Government (Kitab Al-Imara) [020:4649] It has been reported on the authority of Amr b. al-‘As that the Messenger of Allah (may peace be upon him) said: All the sins of a Shahid (martyr) are forgiven except debt.
2. The Book of Faith (Kitab Al-Iman) [001:0209]
It is narrated on the authority of ‘Umar b. Khattab that when it was the day of khaibar a party of Companions of the Apostle (may peace be upon him) came there and said: So and so is a martyr, till they happened to pass by a man and said: So and so is a martyr. Upon this the Messenger of Allah remarked: Nay, not so verily I have seen him in the Fire for the garment or cloak that he had stolen from the booty, Then the Messenger of Allah (may peace be upon him) said: Umar son of Khattab, go and announce to the people that none but the believers shall enter Paradise. He (‘Umar b. Khattab) narrated: I went out and proclaimed: Verily none but the believers would enter Paradise.
We see that in the first hadith the sins of martyr will be forgiven except debt and the second hadith says since he stole from the booty his sins will not be forgiven.
Praise be to Allah.Firstly:
Muslim (1886) narrated from ‘Abdullah ibn ‘Amr (may Allah be pleased with him) that the Messenger of Allah (blessings and peace of Allah be upon him) said: “The martyr will be forgiven for everything, except debt.”
And Muslim (114) narrated that Ibn ‘Abbaas said: ‘Umar ibn al-Khattaab told me: On the day of Khaybar, a group of the companions of the Prophet (blessings and peace of Allah be upon him) came and said: So and so has been martyred, So and so has been martyred, until they came to a man and said, So and so has been martyred, but the Messenger of Allah (blessings and peace of Allah be upon him) said: “No. I saw him in the Fire because of a cloak or abayah that he stole from the war booty.” Then the Messenger of Allah (blessings and peace of Allah be upon him) said: “O son of al-Khattaab, go and call out to the people that no one will enter Paradise except the believers.” So I went out and called to them, saying: “No one will enter Paradise except the believers.”
These two saheeh hadiths were narrated by Muslim (may Allah have mercy on him) in his Saheeh. There is no contradiction between them, praise be to Allah. The first hadith indicates that the martyr will be forgiven for all the sins he committed with regard to matters between him and his Lord, except for debt; that will not be forgiven, because it has to do with the rights of people, and sins having to do with the rights of people cannot be expiated by martyrdom.
An-Nawawi (may Allah have mercy on him) said:
The fact that the Prophet (blessings and peace of Allah be upon him) said “except debt” refers to all the rights of other people, and highlights the fact that jihad, martyrdom and other righteous deeds do not expiate sins having to do with the rights of other people; rather they expiate sins having to do with the rights of Allah, may He be exalted.
End quote from Sharh Muslim (29/13)
Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: With regard to the other saheeh hadith, which says that the martyr will be forgiven for everything except debt, what we learn from it is that martyrdom does not expiate shortcomings in paying the dues of other people and that falling short in paying the dues of other people does not rule out attainment of martyrdom, because martyrdom does not mean anything other than that Allah will grant a special reward to those who attain that status, and will grant them extra honour. The hadith clearly states that Allah will pardon the martyr for everything except shortcomings in paying the dues of other people. So if we assume that the martyr has some righteous deeds to his credit, and martyrdom will expiate his bad deeds, except his shortcomings in paying the dues of other people, then his righteous deeds will benefit him in balancing out what he owes to others, and his status of martyrdom will remain unaffected. But if he does not have any righteous deeds to his credit, then he is subject to the will of Allah. And Allah knows best.
End quote from Fath al-Baari (193/10)
At-Turbashti said: What is meant by debt here is that by which he is bound of the rights of other Muslims, because the debtor is not more deserving of warning and demands than the transgressor, usurper, betrayer or thief.
End quote from Tuhfat al-Ahwadhi (302/5)
Secondly:
The booty is one of the rights of other people; in fact it is one of the greatest rights of people, because it has to do with the public wealth. Al-Hijaawi said in az-Zaad (p. 97):
Booty is acquired by seizing it in battle; it belongs to the fighters who were present in the battle. The khums (one fifth) is to be taken from it, then the remainder of the booty is to be divided, with each infantryman getting one share and each horseman getting three shares – one share for him and two shares for his horse. The army should have a share of the booty captured by expeditionary forces, and latter should have a share of what the former captures. End quote.
The word ghulool refers to stealing from the war booty before it has been shared out. An-Nawawi (may Allah have mercy on him) said: Ghulool means betrayal; the original meaning is stealing from the war booty before it has been divided. End quote.
Martyrdom does not expiate stealing from the war booty, because martyrdom does not expiate sins having to do with the rights of other people, as explained above.
The questioner regards stealing from the war booty as a sin other than debt, but in response it may be said that stealing from the war booty is indeed a sin that has to do with the rights of other people, because what is meant by debt in the hadith refers to the rights of other people, not only debt in the usual sense.
Some of the scholars are of the view that stealing from the war booty means that the one who stole it cannot be called a martyr, because as a result of this act he does not deserve to have all his sins forgiven.
An-Nawawi (may Allah have mercy on him) said:
Stealing from the war booty rules out the giving of the title of martyr to anyone who stole from the war booty, if he is killed. End quote.
Al-Qaari (may Allah have mercy on him) said:
That is subject to further discussion, because there is no indication in the hadith that he is not a martyr. How can that be the case when he has been killed fighting for the sake of Allah and serving the Messenger of Allah (blessings and peace of Allah be upon him), and it is not stipulated that the martyr should be without sin or debt, according to scholarly consensus?
End quote from Mirqaat al-Mafaateeh (6/2583)
It may be said that stealing from the war booty deprives the martyr of attaining the highest status of martyrdom, at which all one’s sins are forgiven, even if that does not deprive him of the virtue of martyrdom altogether.
For more information and an explanation that the seriousness of debt should not be underestimated, please see the answer to question no. 144635
And Allah knows best.