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What you are looking to do is modify the existing child support order. Texas has a "Motion to Modify" that you can use in this instance. You can find it on www.texaslawhelp.org here http://texaslawhelp.org/resource/modification-kit.
You will need to notify the mother via personal service and also the Attorney General (usually by mail is sufficient) that you are asking to modify the support. His reasons for modifying would be that your fiance is the caregiver for his daughter and the mother is no longer entitled to support.
He should have a pretty good case if he's had physical custody for this long. The more proof he has of this the better. There is no way to do this without notifying her. He can do this on his own, but hiring a lawyer who is well versed in handling child care issues would be able to expedite this process and would be worth the cost. You can use Avvo.com to find lawyers that offer free consultations and many lawyers these days allow payment plans.