What is the Sharia ruling regarding properties registered in the wife's name, but purchased with the husband's money, and over which the husband's agency remained valid until his death; are they considered a gift or an inheritance?

What is understood from the question is that the husband's action was not a transfer of ownership to the wife, but rather an authorization from him for her to manage his properties. The nominal writing in official documents under the wife's name for the aforementioned purpose is not a sale. Therefore, the properties remain the husband's ownership and are included in his inheritance, and his parents have the right to their legal share of the inheritance.