Is the debtor absolved of his debt if he bequeaths to his mother that she pay off his debt after his death, and she agrees to that?

If someone borrows money with the intention of repaying it, but becomes unable to do so, Allah will make it easy for him to repay it, or will repay it on his behalf if he dies without having repaid it. This is based on the Prophet's (peace be upon him) saying: "Whoever takes people's money intending to repay it, Allah will repay it on his behalf; and whoever takes it intending to destroy it, Allah will destroy him." As for the hadith: "The soul of a believer remains suspended by his debt until it is paid off on his behalf," it is understood to apply to someone who left behind an estate. And a mother bearing the debt does not clear the debtor's liability unless she actually pays it off on his behalf.