Sorry for taking so long to respond.
I am not completely sure what you want to achieve. If you want to use posterior of one model as a prior for another, that’s generally non-trivial (e.g. see Composing Stan models (posterior as next prior))
I think the best way is to figure out how to build a bigger model that fits everything at the same time (i.e. using Y and Z only for B, but fitting A at the same time). One way to do this is in brms is to add a new variable (say isB) that is 1 for students in B and 0 for others. Then you put whatever values you like for Y and Z for A and then use isB + isB:Y + isB:Z in your formula. This way Y and Z only ever affect estimates for B. But obviously details and best approach would depend on the details of your model.
Does that make sense?