Is the husband obligated to pay the full amount of the "jam'iyyah" (rotating savings and credit association) that his wife joined with her mother, knowing that the wife's mother spent a large portion of the money without his permission, and he had intended to pay off a debt of his with this money? And is he sinful if he does not pay the remaining amount?

It is not permissible to abstain from paying the remaining installments of the association, as it is a debt owed by the participant. Neither the wife nor her mother has the right to dispose of the husband's money without his permission, as long as he spends it in a reasonable manner. The mother is responsible for the funds she did not hand over to the husband.