Luigi Mangione Faces Federal Charges, Murder Through Use of Firearm, Stalking

2:30 PM PT -- The federal U.S. Attorney's Office for the Southern District of New York said in a press release ... the state of New York's separate prosecution against Luigi Mangione is currently expected to proceed to trial before the federal case.

Luigi Mangione just arrived in New York City after he waived extradition in Pennsylvania today, and was promptly slapped with a federal criminal court complaint.

According to the complaint filed by federal prosecutors in the Southern District of NY, Mangione is charged with murder through use of a firearm, two stalking charges, and a firearms offense.

Mangione is awaiting his first appearance in federal court after the complaint was unsealed earlier this morning. Mangione stands accused of shooting and killing UnitedHealthcare CEO Brian Thompson.

In the complaint, federal prosecutors allege Mangione traveled across state lines, from Atlanta to Manhattan, on a bus prior to the shooting. He's also accused of using a cell phone and the internet “to plan and carry out the stalking, shooting, and killing" of Thompson.

As we reported ... Manhattan D.A. Alvin Bragg has filed felony state charges for murder with intent to "evoke terror" ... as well as other serious crimes.  A grand jury returned a indictment against Mangione earlier this week.

Karen Friedman Agnifilo -- a prominent defense attorney in NY -- released a statement after the report came out ... saying the feds' decision to pile on to the charges Mangione already faced is highly unusual.

While the death penalty was abolished in New York back in 2007, it's still legally allowed on a federal level ... so, feds could pursue the harsh punishment.

As you know ... Thompson was shot by a gunman multiple times on December 4, and a statewide manhunt began for the shooter.

Eventually, Mangione was arrested in Pennsylvania after a McDonald's employee called the cops. He was locked up in SCI Huntingdon -- a correctional facility near Altoona, PA.