Hindu adoption act

If a son is adopted then after adoption the son till the age of 62 years uses his natural fathers name at many registered sale deeds of government now this adapted son dies by the age of 66. Does the adaptive sons legal heirs have any right of the property of the mother ( who has adopted ) adaptive son when he was not adopted. First question. Suppose A & B are not having any child. In 1959( B ) means wife purchased 2 properties and sold one and one was remaining and after that by 1965 they adopted a son named C. Now C is selling a property purchased from B( mother who has adopted ) earlier his adoption and C is selling that property in parts till 2010 by using his natural father name at the age of 62 in those registered sale deeds so now C died at the age of 66. Now the legal heirs of C will have the right of the remaining property of B as b also died earlier before C died. As C used his natural father name and self admitted it in the registered sale deeds till the age of 62 so how come he can become child of 2 parents. So now the legal heirs of C has the right on B ( mother who adopted C ) remaining property.