My question involves adoption law for the State of: Texas

My husband and I has been living for seven years and married for five years. After getting married we decided to moved in the U.S. to live and migrate my child with me. My child was only four years old when he met my husband and since then my husband stands a like real father to my child. All the financial needs, care and love was solely supported by my husband while raising my child with him. The biological father never gave any type of financial support, since the time of our separation back in 2002. NO communication made except when i asked him to sign the unconditional consent and legal costudy under my name to live with me in the U.S. My daughter will be 11 years old on Aug. Now my husband is planning to adopt her to make her a real daughter, their relationship got to where like more than like a real father-daughter relationship. My child was been very vocal to use her stepfather surname, she wanted to have a last name same with us.

Currently we are holding a immigrant visa and applying our citizenship this year. Could be the adoption to my child will be more easier to do the process if we wait till our citizenship get done? Can we file the adoption without his biological father consent, because he's living outside the U.S.? Can we consider this an abondonment of parental obligations? Please advice.

Thank you.