Change mesh of a rigged body with a new one

Hi everyone, I’ve been struggling with this one and I really don’t know how to continue.

I have these two models, they have its own skeleton but it is also very similar (same names too). I want to put the left one into the right one. Just that.

I tried making a new one with the parts combined and then applied skin utilities using the original model, but that didn’t work.
I also deleted the bones from mesh A and created a skin modifier using the bones from the original model, skin utilities and that didn’t work :(.

Which is the best way to do this? I want to create several bodies for this model from different skeletons and I don’t want to make a new rigging for each one.

Many thanks in advance!