Mystery Still Surrounds J.F.K. Assassination, 36 Years Later Today marks the 36th anniversary of the death of President John F. Kennedy and even now there is mystery surrounding the details of his assassin. Hours after the president was shot, F.B.I. agents reportedly listened to a tape of a phone call that a man identifying himself as "Lee Oswald" had placed to the Soviet Embassy in Mexico City. Government records suggest the agents made a startling discovery -- the voice on the tape was not Oswald's. Several assassination researchers have some theories as to why anyone would impersonate Oswald. One theory is that a C.I.A. officer could have impersonated Oswald and called the Soviet Embassy to fish for details about what Oswald had recently been doing in Mexico City. Another is that someone may have been trying to link Oswald to the K.G.B.'s assassination unit.