This could be considered misinformation because it is misinformation. We can in fact measure these things and the mRNA vaccines have been demonstrated to generated a robust immune response including memory B cells:

https://immunology.sciencemag.org/content/6/58/eabi6950 https://science.sciencemag.org/content/371/6529/eabf4063

Thank you for sharing, that is effectively what I had been looking for! Please ignore my misinformation.

That second link seems to be about natural immunity not vaccines.