Linked claims

My client was in receipt of irESA with the Support Component.  Her ESA was stopped as she was found to living with her partner.  ESA stopped from about 2 years ago and there is an overpayment.  (Client is appealling the entitlement decision but I am not too hopeful…). 

The alleged partner moved out and C reclaimed ESA.  She has been told she will have to wait 3 months to get her SC back. 
My initial thought was that she should have got back the SC straight away as she has always been in the Support Group (and received credits on this basis).  The gap was in her actual entilement to benefit.  We asked the ESA office to reconsider their decision.  I am now not sure I am correct. 
Any advice please?