I am thinking this figure
which can also be drawn like this
How does HBeAg change to Anti-HBe?
There are some triggers that stimulate Anti-HBe production after HBeAg level is done. I think they can Anti-HBc. There must be other mechanisms too.
I'm not sure that I have understood the question but ...
HbeAg is a secreted variant of HbcAg (the core antigen of HBV). Unlike HbcAg, HbeAg is found in the blood. I believe that it is produced as a result of a splice variant of the corresponding RNA.
The phenomenon described in these Figures is an example of seroconversion. Before seroconversion the antigen is detectable in the blood but there is no antibody directed against it; after seroconversion there is antibody but no antigen.