The three were stopped on a rural road northwest of the Border Patrol's inland Falfurrias checkpoint.
The Border Patrol says Mustafaj became a legal permanent resident after coming to the U.S. as a refugee.
His brother, whose name was not released, was found to be under a deportation order and was held for deportation proceedings, said Border Patrol spokesman John Lopez. The third man was in the U.S. legally and was released.
Details on the New York City killing were not immediately available from the Border Patrol.
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