Your problem, Einstein, is to forget that the jab is not a vaccine but only mRNA. Your problem is to address the question: do antibodies from natural immunity attach to the spike mRNA of the "vaccine"?
Time windows should be compared, @ 3 mo. the mRNA starts to disappear. That is, if there are no previous antibodies against it, which may accelerate the degradation of the spike mRNA much sooner.
You seem confused about the process we're discussing here ...
An "antibody" is a special type of protein ... and
ALL proteins are made using mRNA ... this mRNA is made in the nucleus using the DNA there as a template ...
THE VIRUS alters this DNA to make it's own mRNA, and thus it's own proteins ... and it's these virus proteins that our bodies react to, we have our own immunization system ...
Yes, the virus itself produces these proteins and we obtain immunity just by having caught the virus ... sometimes we can also take the virus, kill it, and inject it into people*, the proteins remain, just the virus is dead so it won't infect us, the immunization reaction in our body is the same ...
including the mRNA step ...
All we're doing is skipping the part that included the virus' genetic material ... providing the cell with the mRNA directly, letting the body's immunization system target the protein that produced without all the damage to the host cell's own DNA ...
We should only expect a year's worth of immunity ... no matter how we achieve it ... SARS is like the common cold in this respect, and best is if it doesn't cause symptoms ... looks to me like SARS is evolving towards this, less deadly and thus less likely to encounter vaxxed folks ...
=====
The answer to your question then is the antibodies from natural infection are
identical to the antibodies formed with any and all vaccines ... the mRNA step is very transient ... each molecule can only be filled up with tRNA so many times ... and then it's broken down into it's component RNA and reused ... and RNA has many uses in the cell ...
* = Injections themselves carry risk ... why doctors ask you sit in the waiting room for 20 minutes after ... just to make sure ...