Puckett was caught Monday at Mayo's apartment. She's charged with hindering apprehension.
Investigators believe Puckett had access to a banned cell phone to help him escape last week from the Stiles Unit in Beaumont, about 75 miles northeast of Houston.
The head of the Texas prison system, Brad Livingston, on Tuesday asked for a demonstration at the Stiles Unit of technology designed to block or manage cell phones.
Puckett since 2002 had been serving 30 years for aggravated assault of a police officer.