Story highlights The undocumented immigrant was acquitted last month of murder charges

He will be released into federal custody, the public defender's office says

(CNN) Jose Ines Garcia Zarate, the undocumented immigrant acquitted last month in the death of Kate Steinle, was sentenced on a firearm charge Friday as his case moves from the state to the federal level.

Garcia Zarate, 45, was sentenced to three years in prison on Friday for a lesser state firearm charge he was convicted of in December in connection with the Steinle case.

But while Garcia Zarate has enough credits of served time to cover his sentence, Tamara Aparton, spokeswoman for the San Francisco Public Defender's Office, said he will not go free. Instead, Garcia Zarate -- who had been deported from the United States five times before Steinle's death -- will be put into federal custody.

Garcia Zarate was convicted last month of being a felon in possession of a firearm -- the charge he was sentenced for Friday -- in connection to Steinle's death in at San Francisco's Pier 14 in July 2015. But the jury acquitted Garcia Zarate, a Mexican citizen, of the more serious charges of murder, involuntary manslaughter and assault with a deadly weapon.

Friday, the judge also denied Garcia Zarate's motion for a new trial, said Alex Bastian, a spokesman for the San Francisco district attorney's office.

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