The first crematory built in the state of Texas was located in San Antonio and was built by the San Antonio Cremation Company. The general location was east of the historic cemeteries at the corner of East Crockett & North Palmetto Streets. The building was constructed after 1885, but before it could be used it was destroyed by arson. I have been unable to find a photograph or rendering of the building.
In 1922, Mission Burial Park constructed a chapel on their grounds that contained a crematory, and this became the state's first operational crematory. The facility still stands, though cremation operations have been moved to another part of the cemetery. The building is pictured below as illustrated in an issue of Park & Cemetery (Modern Cemetery) Magazine in 1922.