My father owns a flat that’s currently registered in my mother’s name. Can he write a letter to the society stating that I will inherit the flat after my mother? What are the legal steps involved in this process?

Under Indian law, a father can’t unilaterally declare a future inheritance. Your father can make a will bequeathing the flat to you after your mother’s demise. He should consult a lawyer to draft a legally valid will and register it to ensure it’s legally binding.