Is the act of forgiving a debtor's debt with the intention of charity for the sake of Allah considered an acceptable charity?

If the debtor is in straitened circumstances, then absolving him and waiving the debt for him is one of the best forms of charity. Allah Almighty Himself referred to absolving someone in straitened circumstances as charity when He said: "And that you remit [the debt] as charity is better for you, if you only knew." Many prophetic traditions have been reported encouraging granting respite to someone in straitened circumstances and overlooking their debt, such as his (peace be upon him) saying: "Whoever wishes that Allah shades him on a day when there is no shade but His, let him ease the burden of one in difficulty or waive the debt for him." However, if the debtor is well-off, your waiving the debt for him is considered a gift and not charity.