Oswald’s whereabouts at this time would become critical because of the statements of Mrs. Sylvia Odio:

Mrs. Odio and her two sisters were Cuban Exiles and members of the Cuban Revolutionary Junta (JURE).

The FBI contacted Mrs. Odio after hearing about a conversation she had with a neighbor about an encounter with Lee Oswald. She would testified that in late September 1963, three men came to her apartment in Dallas, They knew about her father who was a political prisoner of the Castro regime. One of them asked for her help in preparing a letter soliciting funds for JURE activities. He also asked if she was "working in the underground." She told them she was not. Two men identified themselves by their fictitious underground "war names." The one that did the talking was "Leopoldo" and appeared to be Cuban, the second man who he called Angelo appeared to be Mexican and the third man was introduced as "Leon Oswald." And appeared to be American, and she was told that he (Leon) was very much interested in the Cuban cause. She was also told that they had just come from New Orleans and that they were about to leave on a trip.

Mrs. Odio’s sister who also saw the men in their hallway, believed that the third man was Lee Harvey Oswald.

Mrs. Odio also testified that Leopoldo called her the next day and told her that it was his idea to introduce the American into the underground "because he is great, he is kind of nuts." He also told her the American had been in the Marine Corps and was an excellent shot, the American said the Cubans "don’t have any guts because President Kennedy should have been assassinated after the Bay of Pigs.

This whole incident became another timing problem for the Warren Commission, they had to find a way to get Oswald from New Orleans to Houston and then to Mexico with out having been in Dallas. However they did make an attempt to find the three men but the issue was never resolved.
 

According to the Warren Commission:

Oswald could not have been in Dallas on the evening of either September 26 or 27, 1963. There is strong evidence that on September 26, 1963, Oswald traveled on Continental Trailways bus No. 5133 which left Houston at 2:35 A.M. for Laredo. The bus was scheduled to arrive in Laredo at 1:20 P.M. on September 26, and Mexican immigration records show that Oswald in fact crossed the border at Laredo to Nuevo Laredo, Mexico, between 6 A.M. and 2 P.M. on that day. Two English passengers, Dr. and Mrs. John B. McFarland, testified that they saw Oswald riding alone on this bus shortly after they awoke at 6 A.M.

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Lee Harvey Oswald PT-I PAGES 1 - 5			Lee Harvey Oswald PT-II PAGES 1 - 4

1 American, Marine, defector 2 Oswald in the U.S.S.R. 3 Returns, Attempt on Gen. Walker

4 De Mohrenschildt,  joins FPCC then offers help to anti Castro groups 5 Arrested in New Orleans, Radio interview

1 Lee Oswald and Jack Ruby's INTERESTS IN CUBA 2 CUBA the MOB the CIA and the Watergate Break-in  3 David Ferrie, Lee Oswald Connection