On November 27, the Attorney General's Office issued an arrest warrant against Garcia for the crime of illicit enrichment.
He was arrested in Dallas in December 2019 and later transfer to New York where he was accused of five crimes, including "conspiracy to drug traffic" and "false declarations" to migrations authorities.
He has pleaded not guilty to the U.S. charges which can cause him a life imprisonment sentence.
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The case against Garcia is based on his alleged collaboration with the Sinaloa Cartel founded by Joaquin Guzman better known as "El Chapo Guzman".
He is due to attend court on February 17 next year to present testimonies before the U.S. judge Brian Cogan.
If approved, Garcia's extradition to Mexico will follow that of former Defense Secretary General Salvador who also faced a trial for drug trafficking in the U.S. and returned to the country after a request by Mexican authorities.