A & B Lived Together as Husband and Wife Without

A & B lived together as husband and wife without the benefit of marriage. For a few months before his death, A was writing his autobiography and stated that he loved B so much and because of that, they decided to live together as husband and wife, but planned to marry. At the time he was writing his autobiography, B was pregnant and he stated in his autobiography that he was the father of the child inside the womb of B. He died without finishing it and failed to sign the same. Two (2) months thereafter, the child C, was born, hence, B sought to register the child under the name of A but the Local Civil Registrar refused, hence, she filed a suit for mandamus to compel the registrar to register the child under A's name. She testified as narrated above; D, the father of A testified that during the lifetime of A he lived with B and she was pregnant at that time. E the brother of A likewise testified along the same line. Is the action of B correct?

A) The child cannot be registered under A's name because the autobiography was not signed.
B) The child cannot be registered under A's name otherwise, it would be easy for a woman to vest legitimate status upon a child even if he is illegitimate.
C) The child can be registered under A's name because of the principles in the rules of evidence of pedigree declaration against interest supported by the autobiography and the testimonies of D & E.
D) The child cannot be registered under A's name because an unsigned document is not evidence of recognition.