According to Cruau, the man killed by police and identified as Charley Saturmin Robinet was not a citizen of France, but used a fake identity and a French passport to come to the United States in the late 1990s.
The identity theft is said to have been revealed when the man claiming to be Robinet was arrested for robbing a branch of Wells Fargo Bank in Ventura County, California back in 2000.
Cruau was quoted as saying that the real Charley Saturmin Robinet was alive and currently living in France.
On Sunday, Los Angeles police shot and killed the as-yet-unidentified homeless man when, approached by officers, he engaged in what appears in a video posted online to be violent physical resistance. The shooting triggered a rally near the Los Angeles Police Department headquarters.
The incident in Los Angeles is the latest in a series of fatal casualties when US police have used what many are calling excessive force. Since the summer 2014, the country has seen a wave of protests calling for police accountability in light of the killing of two black men, Eric Garner and Michael Brown, by police in New York City and Ferguson, Missouri.
A scathing report by the US Justice Department scheduled for release Wednesday states that the predominantly white Ferguson Police Department regularly violated the constitutional rights of its black population.