My sister's new husband wants to adopt her son.

My sister's ex husband was the biggest fraud ever. He used his brother's name to get married to my sister, without her knowing. He had been in jail for having sex with a minor, he was older then what he had told her. After he cheated on my sister and left her to care for her their son, she started to investigate his past. She quickly divorced him and got full custody of their son. It doesn't matter because he just doesn't care for their son anyhow. My sister since then got married and her husband has been raising my nephew together, that's the only father my nephew knows now. Now, that they are married he wants to adopt him, but my nephew's biological father can't be found. What are the steps to adopt him. She consulted with a lawyer, but he is asking for $5000.