How to cancel a wrong identity with NSO so that the real origional one can be used. CAN ANY ONE ADVISE THE COSTS

My Filipina Friend who is a OFW working over seas had a Daughter out of Wedlock some 15 years ago the birth of the Child was registered in Hong Kong and the Child was issued a Philippine Passport she took her Child back to the Philippines at the age of 3 months and left her in the care of her Sister inlaw however after 6 months the Sister of my Filipina friend took the child with out permission saying she was borrowing her when my friend discovered this she was very upset but agreed her sister and husband could look after her Daughter on the condition that they would always let her know she was the Mother and they were the Auntie and Uncle which they agreed and she always sent support my friend remarried 10 years ago after she got an annulment at that time she agreed that her sister could continue to look after her Daughter however after about a year she her sister said she change the name of the child just for the school including the surname my friend was upset and did not agree and told her sister to change back the name over the following 9 years she keep promising to change the name back to the real name which was already registered in NSO, now she discovered that when the child was 2 years old they made a late birth declaration with the help of a Mid Wife and registered with the NSO! this was only discovered 3 months ago and my friend also discovered that her Daughter did not know she was the real mother as in all this time she thought the Auntie and Uncle were her Mother and Father! now the Daughter refuse to change the name to the real name and in fact she is registered under to identities one the real and the second a false one, my friend wants to cancel the fake ID created by her Brother in Law and Sister but does not want to prosecute them, she just wants to settle the case by canceling the wrong ID and she also wants to know can she take her Daughter back even if her Daughter wants to keep the wrong ID and remain with the Fake Mother and Father, Please advise what are the Mothers rights in this case and how could she go about dealing with this and the costs involved?