Tex. Tax Code § 26.1125

Sec. 26.1125. CALCULATION OF TAXES ON RESIDENCE HOMESTEAD OF 100 PERCENT OR TOTALLY DISABLED VETERAN. (a) If a person qualifies for an exemption under Section 11.131 after the beginning of a tax year, the amount of the taxes on the residence homestead of the person for the tax year is calculated by multiplying the amount of the taxes that otherwise would be imposed on the residence homestead for the entire year had the person not qualified for the exemption under Section 11.131 by a fraction, the denominator of which is 365 and the numerator of which is the number of days that elapsed before the date the person qualified for the exemption under Section 11.131.

(b) If a person qualifies for an exemption under Section 11.131 with respect to the property after the amount of the tax due on the property is calculated and the effect of the qualification is to reduce the amount of the tax due on the property, the assessor for each taxing unit shall recalculate the amount of the tax due on the property and correct the tax roll. If the tax bill has been mailed and the tax on the property has not been paid, the assessor shall mail a corrected tax bill to the person in whose name the property is listed on the tax roll or to the person's authorized agent. If the tax on the property has been paid, the tax collector for the taxing unit shall refund to the person who was the owner of the property on the date the tax was paid the amount by which the payment exceeded the tax due.