V
There is no mechanism to move a claimant from ESA to JSA. I suspect you saw JSA on a recent payment to your partner, if this is the case then it just means that the DWP made an ad hoc payment, the ESA payment system sits on top of the JSA.
The change to the ESA would likely be the removal of at least one SDP payment.
There is information in the PIP area that covers requesting an MR and then an appeal, if necessary.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems