Can my nieces mother voluntarily relinquish rights?

My 5 year old niece has lived with my wife and I for 2 years, the last 6 months of it in the state of TX. Her father (my brother) is deceased and mother, who lives in Washington state now wants to relinquish all rights due to not being able to care for the child/addiction issues. I have contemplated adopting her but same sex adoptions seem harder. I just need to know what steps need to be taken to do this all legally. Her mother pays child support to the state and my niece receives a portion of that monthly, naturally I am aware this will stop and am fine with that, I added the fact in so that anyone answering would be aware that the state in fact knows the child has been in my care.