(CNN) -- A man considered a prime suspect in the death of a Virginia woman and the abduction of her daughter waived extradition Tuesday and will return from California, authorities said.
Jeffrey Scott Easley, 32, appeared in San Francisco Superior Court and decided to return to Roanoke, where he faces abduction and credit card fraud charges, Roanoke County spokeswoman Teresa Hall said.
He will probably return Wednesday or Thursday, Hall said.
Police say Brittany Mae Smith, 12, was abducted and taken on a weeklong cross-country trek.
The girl's father, Benjamin Smith, expressed gratitude Monday to the numerous people who worked on the case and who publicized the names and faces of Brittany and her alleged abductor. He singled out Theresa Shanley, who recognized the pair outside a San Francisco supermarket, as "my hero."
Two detectives from Roanoke County escorted the girl from California back to Roanoke on Monday, Hall said.
Roanoke County police Chief Ray Lavinder has called Easley a "very good suspect" in the death of Tina Smith, Brittany's mother.
Police believe that 41-year-old Smith, who was Easley's girlfriend, was killed between the morning and evening of December 3, Lavinder said. On that day, surveillance video shows Easley and Brittany Smith shopping for a blue domed tent at a Wal-Mart in Salem.
Lavinder said authorities believe that the two left Virginia, heading toward California, that night or early the next day. They traveled cross-country in Tina Smith's silver 2005 Dodge Neon sedan, which was found in a parking lot adjacent to San Francisco International Airport after authorities found Brittany Smith and Easley.
The pair were holding up a cardboard sign and asking for money when they were spotted, Lavinder said. The Safeway was within walking distance of the makeshift campsite containing the tent in which Easley and Brittany Smith had been staying.
Easley did not resist when police arrested him shortly after 2 p.m. Friday, San Francisco police Officer Albie Esparza said.