When the immune system is primed after first does of an inactivated vaccine, how fast do memory b cells identify and destroy the antigen following the forth dose of the inactivated vaccine? is this reaction immediate?

Hypothetical: Different people have different immune responses and immune response is under genetic control. Most people would have an adequate immune response under the circumstance you described. It also depends on the nature of the antigen. An antigen may be hidden inside cells and not accessible to antibody. If you could be more specific it may be helpful. Wish you good health!