Whew. So much nonsense and falsehoods in one short post. Here is the list of the contents of Oswald's wallet: https://www.history-matters.com/archive/jfk/wc/wcvols/wh24/pdf/WH24_CE_1986.pdf
The rest of your rambling nonsense is based on a false premise. The sequence of events is that Oswald is identified (he has multiple IDs in his name, a co-worker confirms his identity, and Oswald confirms his name to CT Walker), an agent calls the Dallas FBI with that information ("shortly after 2"), Hosty recognizes Oswald's name, Dallas FBI then "immediately" inform FBI HQ of the suspect's name and that they have a file on him. Hosty, as the agent in charge of Oswald's file, is then understandably dispatched to attend his interrogation. There is no mystery there.
Errrr.... Mr "Smith"....Perhaps you should take a refresher course in elementary arithmetic....basic counting.....Because either you can't count ...or you're a liar....
This list shows Seven ( 7 ) ID cards that have the name Lee Oswald ( or the initials LH Oswald) written on them.
https://www.history-matters.com/archive/jfk/wc/wcvols/wh24/pdf/WH24_CE_1986.pdfThe sequence of events is that Oswald is identified (he has multiple IDs in his name, a co-worker confirms his identity, and Oswald confirms his name to CT Walker), an agent calls the Dallas FBI with that information ("shortly after 2"), Hosty recognizes Oswald's name, Dallas FBI then "immediately" inform FBI HQ of the suspect's name and that they have a file on him. Hosty, as the agent in charge of Oswald's file, is then understandably dispatched to attend his interrogation.
On page 16 of the book
Assignment : Oswald Written by FBI Agent James Hosty.... ( You may recall that Hosty was in the thick of it)
Hosty wrote....
TIME 2:15 P. M. "A hand clutched my elbow. I spun, Howe was in my face. "They've just arrested a guy named Lee Oswald, and they're booking him for the killing of the policeman over in Oak Cliff. Officer's name was Tippit." Hosty said that Shanklin was still on on the phone with Alan Belmont at FBI Headquarters in Washington DC. who had told Shanklin that Oswald had been arrested by the DPD, and Shanklin was ordered to send HOSTY over to the DPD.
Since Howe told Hosty that Oswald had been arrested for shooting JD Tippit ( which was NOT under FBI jurisdiction) that information had to have been received by Shanklin in Dallas from FBI headquarters in Wash DC at no later than 2:10 and about five minutes prior to Howe telling Hosty that Lee Oswald had been arrested.