All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
If this debtor is insolvent, then there is no doubt that relieving him of paying off his debt is one of the best forms of charity. Allaah The Almighty Says (what means): {And if someone is in hardship, then [let there be] postponement until [a time of] ease. But if you give [from your right as] charity, then it is better for you, if you only knew.}[Quran 2:280] Allaah The Almighty Describes the acquittal of one who goes through difficulty and relieving him from debt as charity. Ibn Katheer said in his Tafseer: "It is recommended to cancel the debt of the debtor and Allaah Promises the one who does this much good and great reward as He Says (what means) {But if you give [from your right as] charity, then it is better for you, if you only knew}. 'But if you give charity' means: but if you leave your capital completely and relieve the debtor of paying it back (then it is better for you). There are also many Hadeeths of the Prophet, sallallaahu ‘alayhi was sallam to this effect…" He then gave a lengthy account of the Hadeeths that highlight the virtue of giving respite to an insolvent debtor. It is narrated on the authority of Abu Umaamah that the Prophet, sallallaahu ‘alayhi wa sallam, said: "Whoever would be pleased that Allaah Would Shelter him under His Shade on the Day when there will be no shade except His, let him alleviate the debt of an insolvent person or grant him remission." [At-Tabaraani]
It is narrated that Abu Qataadah was owed a debt by a man and, whenever he went to ask him for payment, he used to hide from him. One day, Abu Qataadah came looking for the debtor and a young boy came out. He asked him about the debtor and the boy told him that he was in the house eating Khazeerah (i.e. a kind of food made from meat and flour). Abu Qataadah said in a loud voice, "O so and so! Come out, for I was told that you are in the house!'' The man came out and he asked him, "Why are you hiding from me?'' The man said, "I am going through financial difficulty and I do not have any money.'' Abu Qataadah said, "By Allaah, are you truly facing a hard time?'' He said, "Yes.'' Abu Qataadah then cried saying, "I heard the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, say: "Whoever gives respite to his debtor or forgives the debt will be in the shade of the Throne (of Allaah) on the Day of Judgment.'' [Muslim]
It is also narrated on the authority of Abu Hurayrah that the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, said, "There was a merchant who used to lend the people and, whenever his debtor was in straitened circumstances, he would say to his employees, 'Forgive him so that Allaah may Forgive us.' So, Allaah Forgave him." [Al-Bukhari]
However, if this debtor is well off, then your remittal of the debt is considered a gift and not a charity.