Is it permissible for the manager to benefit from the 10% discount offered by the educational center for the children of the debtor, whose expenses the manager will pay, by deducting the full amount (1000) from the debt after paying 900 to the center, with the knowledge and approval of the center's owners?

There is no harm in agreeing to pay the expenses for the creditor's children as an agency, but the agent must be truthful. It is not permissible for him to profit from a discount unless he has his principal's permission. Therefore, the creditor must be informed of the actual amount paid (900 instead of 1000), and the discount belongs to the principal unless he permits the agent to keep it.