Quay-Sean Hines, 30, is accused of ambushing his former girlfriend, Amelia Laguerre, 33, as she left work in New Hyde Park last week.
Police say in one instance, Hines had essentially stalked Laguerre.
"He immediately came up behind her, shot at her ten times, strangled her nine times," said Nassau County Police Captain Stephen Fitzpatrick.
They say he allegedly had broken into her apartment, and in one instance burned her clothing.
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