Hi,
Sorry I missed this tab. I hoope this reply is still useful.
What you describe is not the way to transfer grooms. You need to use Ground Strands and then collapse the stack with all the modifiers before the grounder.
The idea is to attach the hair roots to the new mesh. However on the modifiers before that the old mesh will still be linked to the groom. This is why I recommend collapsing the stack, to brake that link with the old mesh.
Also, I recommend transferring the groom to the final animated model instead. Animating the character with the hair in the same scene (Hair + rigging) can be heavy.