Armstrong was arrested in Costa Rica on June 29 and extradited to the US on July 2 to face murder charges.
CNN reached out Thursday to an attorney listed as Armstrong’s representative.
Wilson was found dead of multiple gunshot wounds at a friend’s home, authorities said. She had told her friend she was going for an afternoon swim with Colin Strickland, 35, a professional cyclist and friend of Armstrong’s. He told police he and Wilson swam and had dinner and he dropped her off at her friend’s house, according to an arrest affidavit in Travis County District Court.
Investigators said romantic jealousy may have been a motive for the killing.
Armstrong’s trip to Costa Rica took her from the capital of San Jose to Jaco Beach and Santa Teresa Beach, said Deputy U.S. Marshal Brandon Fila, a spokesman for the U.S. Marshals’ office in Austin. Both Jaco Beach and Santa Teresa Beach are on the Pacific coast.
“It was discovered that Armstrong used different names, aliases, under the alias Beth Martin, Liz and Ari Martin,” Filla said during a press conference Thursday. Armstrong used those names at yoga studios and other accommodations, he said.
Filla did not identify which passport Armstrong was allegedly using.
While in Costa Rica, Armstrong was “really trying” to build something so she could teach yoga, Filla said.
But investigators were on her trail, using “old-fashioned law enforcement techniques,” he said.
Investigators focused on the bus Armstrong took from the San Jose airport. “They knew the route of that bus and that’s where they started the boots on the ground,” he said.
She also used pseudonyms for her signature, and “that really started the path to narrow down a path to Kaitlin Armstrong,” Filla said.
She had also changed her physical appearance. “She dyed her hair brown. She cut her hair closer to about shoulder length,” Filla said.
Officials went door-to-door conducting interviews at yoga facilities and hostels, which led them to Santa Teresa where he was taken into custody.
But life as a fugitive seemed to take its toll.
“Talking to the foreign nationals there in Costa Rica, I would say she was exhausted,” Filla said, adding, “When she was confronted by uniformed officers in Costa Rica, she didn’t give her real identity at first, but when she was taken into custody and questioned , you know, a few minutes later, and she finally confessed her true identity.”
Armstrong was arrested for violating Costa Rica’s fraudulent use of passport laws, according to Filla.
He is being held at the Travis County Jail in Austin, according to jail records. Armstrong also faces an additional federal charge of unlawful flight to avoid prosecution.
CNN’s Rebekah Reiss and Steve Almasy contributed to this report.