A jury has found Dontae Morris guilty of murdering Derek Anderson in an alleged dispute over drugs.
Prosecutors will now be able to inform the jury of Morris' previous murder convictions, and the defense will argue why he should be spared the death penalty.
Morris is accused of murdering five people in a 2010 spree that culminated in the shooting deaths of two Tampa police officers.
Jurors in the Anderson trial were not told Morris has been sentenced to death for killing Officers David Curtis and Jeffrey Kocab during a traffic stop or that he has received life in prison for killing another man, Rodney Jones.
Morris awaits trial in a fifth murder case.