The 50-year-old death row inmate had faced lethal injection Thursday for the fatal shooting of Garland police officer Michael Moore during a bank robbery 12 years ago.
Moore was fatally wounded when one of four bullets that hit him struck above the top edge of his protective vest. Mosley was shot in the wrist by another officer waiting outside the bank and was arrested in the parking lot.
A state district judge in Dallas has reset Mosley's execution for Sept. 24.
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