How do I get custody of my step son in the state of Texas with out having to go to court?

My step son has been living with me since the end of february. His mom wants to sign custody or guardianship whatever it takes for me to change his school, get him on Medicaid, and add him to my food stamps to be able to continue feeding everyone. If there is a paper she can sign then she is willing to sign it. His dad is in federal prison for the next 2 1/2 years. He is 15 years old, but he wants to be with me and his mom doesn’t want him for some reason. He is a good kid and needs more guidance in his life. I don’t want her to get in trouble for anything though and would rather try to take care of it outside of a court room. Thank you!