Step 1: Understanding the Concept:
The question asks who among the given options is not recognized as a legal guardian (wali) of the property of a minor under Muslim personal law.
Step 3: Detailed Explanation:
Under Hanafi school of Muslim law, the legal guardianship of a minor's property follows a specific order of priority. The recognized legal guardians are:
1. Father: He is the primary and natural guardian.
2. Executor appointed by the father's will: The person designated by the father in his will to be the guardian.
3. Paternal Grandfather: The father's father.
4. Executor appointed by the paternal grandfather's will: The person designated by the grandfather in his will.
A brother is not recognized as a legal guardian of the property, although he can be a guardian of the person (for custody/hizanat) in certain circumstances. Other relatives like the mother or uncle are also not legal guardians of property, though a court can appoint them as such.
Step 4: Final Answer:
The father, the executor appointed by the father, and the paternal grandfather are legal guardians of a Muslim minor's property. The brother is not.