The law office that they refered you to is either a ca or they own the debt and not JCP. If JCP still owns the debt I think that you have the right under federal law to refuse to deal with the ca and deal only with the oc (JCP). I may be wrong about this though. Hopefully someone else will chime in and clarify this as I do not know what the actual law would be to cite, but have heard this for years.
If the law office actually owns the debt you would have to deal with them. Either way send a DV letter to law office for full media validation. Make the law office prove that they have the legal right to collect the debt.