What should be done with the money left by a deceased orphan who was sponsored, and is it permissible to give it to another sponsored orphan after both of them have exceeded twenty years of age?

If someone dies and has no heirs among the Ashab al-Furood (Quranic heirs) or Asabat (agnatic heirs), then their estate goes to the Muslim treasury (Bait al-Mal) if it exists. If there is no Bait al-Mal, or if it exists but is not organized or managed according to Islamic law, then the estate should be spent on the general welfare of Muslims, charitable deeds, and good causes, or given as sadaqa (charity) on behalf of the deceased. Bait al-Mal is the heir of those who have no heirs. Since the Bait al-Mal is currently non-existent, you should spend what your ward left behind on charitable causes, the welfare of Muslims, sponsoring orphans, and giving charity to the poor and needy. The other orphan is not among his heirs, so he should only be given from it if he is in need.