ABANDONMENT

A friend of my wife gave birth four years ago, while she was staying with us. 3 days after giving birth, she left, leaving us with the baby. We have never heard from her again. Four years have gone by and we have never heard from her, no support, nothing. All this time, the child has been with us, cared for, loved, well-provided for, and treated as if she was our own flesh and blood. My question is, what if the biological mother suddenly shows up? Do we have a right to refuse if she takes the child? What legal remedy do we have? FYI, the child was born out of wedlock and never acknowledged by the father.
Thank you for your advice

adopt the child immediately so that the mother will no longer have claims to her child.