https://www.aarclibrary.org/publib/jfk/wc/wr/pdf/WR_A11_ReportsDPD.pdf
Page 2, paragraph 1, FBI Dallas Chief Bookhout requests that FBI Agent Hosty be allowed to question Oswald because " he knew about these people & has been investigating them"
Page 3, paragraph 2, Oswald complains that FBI Agent Hosty has been accosting and harassing his wife .
Sorry, that is not evidence of anyone monitoring "every move" that Oswald made. James Hosty HIMSELF said he didn't know where Oswald was living during the week. If he didn't know where Oswald lived - the N. Beckley rooming house - then how could he be monitoring Oswald at all? He didn't know he lived there.
And even though he knew Oswald lived with Ruth Paine during the week how is that monitoring "every move" Oswald made? It's not. It's not monitoring any move. Did Hosty know what Oswald did on the weekends? Where Oswald went? Who he met? Of course not.
Hosty testified that he was informed that the Oswalds had moved into the Dallas area (no address given) on October 3. But he NO IDEA where they were living. If he didn't know where they were living how could he be monitoring Oswald at all?
Here is his testimony:
Mr. STERN. What did you do on October 3 and thereafter?
Mr. HOSTY. Well, there wasn't too much to go on, just a woman driving a station wagon with a Texas license plate. I went to the immigration office to check to see if they had any information, tried to determine if we had any persons around the area, I tried to think of anyone who spoke Russian who had a station wagon and who was a friend of Marina Oswald's. I went to Fort Worth and checked in his old neighborhood, Lee and Marina's old neighborhood, attempted to locate Robert Oswald, his brother, and determined that Robert Oswald had left the Fort Worth area, had moved to Arkansas.
I then sent out a lead to the Little Rock office which covered the area of Malvern, Ark., where Robert Oswald was living, and requested that he be contacted to see if he knew where Lee Oswald was. Then I continued checking through the Dallas and Fort Worth area attempting to determine if the Oswalds had returned to the Dallas or Fort Worth areas.
So he had no idea where Oswald was living. None. This is not monitoring "every move" by Oswald. In fact, it's not monitoring any move.
Hosty said he learned on OCTOBER 29TH that the Oswalds were living with Ruth Paine.
Mr. HOSTY. Very much so, yes. I became curious then. Shortly thereafter, on the 29th of October, I received another communication from the New Orleans office advising that they had a change of address for Lee and Marina Oswald to 2515 West Fifth Street, Irving, Tex.
Mr. STERN. You received that information when?
Mr. HOSTY. On the 29th of October.
So from October 3 to October 29th Hosty had no idea where Oswald lived. And he never knew where Oswald lived during the week.
Again, nobody was monitoring Oswald's "every move."