By Deborah Quinn Hensel
HOUSTON (Reuters) - The medical condition of the mother whose four young children died last week after a shooting at the family's Houston-area home has improved from "critical serious" to "serious," police said on Monday.
The shooter -- the mother's husband -- died after apparently shooting himself in the head, Bay City police have said.
The mother is with family and friends and has been told that all four of her children have died, Bay City Police Department spokesman Lt. Andrew Lewis said in a statement on Monday.
The mother, Laura Gonzalez, lost her daughter, Cecilia, 2, and her three sons, Daniel, 3; Miguel, 4; and Sean, 5, said Roxanne Mena of the Harris County Institute of Forensic Sciences.
The shooter has been identified as Jose Avila-Alva, 27, Lewis said on Monday. He had previously been identified as age 24. Avila-Alva, who was from Mexico, was in the United States illegally and had been deported to Mexico in 2006 for unlawful entry into the United States, the statement said.
The weapon used in the November 30 shooting was a .22-caliber revolver that had been reported stolen in 2010 to the Port Arthur Police Department, the statement said.
The week before the shooting, Avila-Alva -- the children's father, according to local media reports -- was reported to police for domestic assault, according to reports in the Houston Chronicle.
His wife was taken to a women's crisis center, but she did not file charges against him and he was not arrested, the newspaper reported.
A vigil for the family was being planned for Wednesday evening in Bay City.
(Additional reporting by Mandy Oaklander. Editing by Corrie MacLaggan and Peter Bohan)