An important question is whether the FBI knew that Clay Shaw was the elusive Clay Bertrand. Here's an FBI memo from March 2, 1967 that seems to indicate they did have information that Shaw was Bertrand.
We can see that one source was Aaron Kohn, head of the Metropolitan Crime Commision. But, who was the other source that Shaw was Bertrand? In an FBI Airirtel, we see that the source was informant 1309-C, which is none other than Joseph Oster, who had once worked for Guy Banister.
So, we can clearly see that Aaron Kohn's identification of Shaw as Bertrand was only based on news sources. New Orleans was a cauldron of rumor, innuendo, and gossip (Indeed, the New Orleans States-Item mentioned Clay Bertrand in a news article on February 22, 1967), and so, Kohn heard from his sources that Shaw was Bertrand. But, he had no special knowledge on that front. Indeed, I have gone through the memos he wrote for the Metropolitan Crime Commission at the National Archives, and I can ensure you that he never believed that Shaw was Bertrand.
Now, about source 1309-C. Why did he believe that Shaw was Bertrand? And who was 1309-C?
Again, according to news sources.
And, who is 1309-C? The FBI's file on 1309-C was 137-2409.
Joseph Oster also talked to Jim Garrison. Here is his statement to the D.A.'s office:
Nothing here about knowing who Clay Bertrand was. That's because it was December 1966 and no one was talking about Bertrand.
Note that Raymond Beck, a former special agent, was now working for Garrison, and informing on what was going on. Also, check out the third page of the memo, Oster states that Jack Martin and Joseph Newbrough [who also had worked for Banister] are "both known to him and personally regards them as mental cases." As you might know, most of Garrison's initial information in his investigation came from Jack Martin.