What I know so far about the way this vaccine works is that by encoding virus' biological signature into the vaccine and injecting it into a subject, the subject's immune system would learn to recognize the virus and develop anti-body against it. Then next time the virus wouldn't break the subject easily because the protection of anti-body.
After getting to know the theory, it looks certainly after injection, it would certainly leave some virus signature (antibody) into the body. During the early stage of virus production one would probably get
IgM+ / IgG+ and after a while becomes
IgM- / IgG+.
So my question is, how long does it take for an individual to get
About IgG and IgM test (quote from here):
IgM and IgG are immunoglobulins produced by the immune system to provide protection against SARS-CoV-2. Anti-SARS-CoV-2 IgM and IgG can therefore be detected in samples from affected patients.
IgM+ / IgG+ : Recent infection with SARS-CoV-2 IgM+ / IgG- : Recent infection with SARS-CoV-2 IgM- / IgG+ : Previous infection with SARS-CoV-2 IgM- / IgG- : No infection or not enough detectable antibodies in the early infection