There are some topics where I think this was discussed extensively. I am aware of the following two for instance:
I think in both cases, the discussion is around how to build a distribution that approximates best the posterior sampled from the “previous model” so that it can be used as the prior for another model and train on new data with those priors from posteriors. And it will rely on certain assumptions sometimes about the shape of the posterior (for instance that it is sufficiently normal etc). If posteriors for A_ and B_ don’t seem to be correlated, you could perhaps simply model them as pair of normals with estimated mean and sd of the posterior sample. Note however in your new model A_ and B_ will also be updated to new posteriors with the presence of new data.