Texas constitution
Article 8: taxation and revenue
Section 1-b

(p) The legislature by general law may provide that a
surviving spouse who qualifies for and receives an exemption in
accordance with Subsection (o) of this section and who subsequently qualifies a different property as the surviving spouse's residence
homestead is entitled to an exemption from ad valorem taxation of
the subsequently qualified homestead in an amount equal to the
dollar amount of the exemption from ad valorem taxation of the first
homestead for which the exemption was received in accordance with
Subsection (o) of this section in the last year in which the
surviving spouse received the exemption in accordance with that
subsection for that homestead if the surviving spouse has not
remarried since the death of the first responder.