Is it permissible to pay Zakat funds to a charitable organization that sponsors an orphan and provides for him annually, then transfers the sponsorship to another orphan after the first one's eligibility period ends?

Money paid to an orphanage is considered Zakat if the intention of Zakat is made at the time of payment, and the orphaned beneficiary is poor, possessing no wealth or provider, because in that case, they are among the poor who are eligible to receive Zakat.