What is the ruling on a person giving their money and properties to an "adopted" child without the permission of the the heirs? Is this considered inheritance or a gift?

It is permissible for a person to donate or give charity from their wealth while in full health and sound mind, without the permission of the heirs, provided they are not in debt, are patient with poverty, or have children who are patient. It is disliked if any of these conditions are missing. It is preferred for a man to bequeath some wealth to the person he intended to donate to, and to leave some wealth for his children, based on the saying of the Prophet, peace and blessings be upon him, to Sa'd ibn Abi Waqqas: "Indeed, for you to leave your heirs wealthy is better than for you to leave them dependent, begging from people."

Adoption is forbidden in Islam, due to the Almighty's saying: ﴿Call them by their fathers' names; it is more just in the sight of Allah﴾ [Al-Ahzab: 5]. It does not entail inheritance or mahramiya (prohibited degrees of marriage). Severe warnings have been reported for those who attribute themselves to other than their father.