FYI I added additional thoughts to my original thread: How best to use a posterior sample as a prior for a future integration in another model? - #14 by perrette
Basically, I take inspiration from two articles on copulas (here and there), and suggest to a) transform the marginal posterior distributions from modelA into normal distributions, b) model the normalized parameters as a MvNormal distribution (and transform back) in modelB. In the case of a long-tailed LogNormal distribution, this is simple (it involves shifting and taking the logarithm), and in the general case it is more complicated but doable provided a parameterized distribution can fit the marginal (and the copula example can be applied: transform to uniform to normal and back with cdf and inverse cdf).