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In order for this change to be legally binding, you and your ex will need to file a Motion to Modify your current custody agreement. Then, once that is filed, you'll need to have the Judge sign the new agreed Final Order. This is the only way to legally formalize the new arrangement and end any child support obligation you may have. You can find the forms to do so at www.texaslawhelp.org.
Note that a letter from her stating that you have custody is not enough. You must go through the courts.