The team behind the ChAdOx-1 vaccine have said that similar vaccines they worked on in the past (SARS1, MERS) triggered the immune system in a different way than getting the virus itself and it's expected that the vaccine-derived immune response would last longer than natural immunity. They have re-tested people they immunized for SARS1 and they still showed immune responses over a decade later.
So the idea is that the vaccine would still be potentially useful to those who have already had the disease.
We should not expect indefinite immunity. With other human coronaviruses that cause colds, immunity typically doesn't last forever, so you can catch the same coronavirus when it comes around again a few years later.
This is not yet known about covid-19. But the claim that you can get it again "three months later" is eye-catching in how short a period that is, and hopefully is quite rare.
I understand that. I am not a doctor either. Let me rephrase my question more concretely and hopefully someone can answer it.
I am curious to know whether the immunity to covid-19 will become stronger or weaker if those people who've already recovered from covid-19 get a vaccine.
Not everyone that (allegedly) gets the vaccine develops antibodies because there are other components of the immune system that destroy the infection prior to the need of developing antibodies.
Even in those that do develop antibodies, they are finding those antibodies are undetectable after some short time period.