Official Error

Just need to know if i am heading in the right direction please. We recieved a Housing Benefit Invoice for a tenant for the period 15/6/09. - 1/2/10 Stating tenant had gone into a nursing home. Although tenant did go into a Nursing home on 9/6/10 this was not made permamnt until 19/8/10. After pointing this out Revenue and Benefits have now stated that the overpayment period is 24/8/09 - 31/1/10. In their correspondence to me Revenue and Benefits have stated that on 12/10/09 and 27/10/09 they were informed by the DWP that tenant was living in a Nursing Home. Tenants daughter attended the Housing Office and terminated the tenancy on 9/12/09 . For some reason Housing Benefit were not informed by ourselves until 2/2/10.
We have now refunded the overpayment for the period 14/12/09 - 31/1/10 as we then knew the tenant was no longer at the property but failed to notifty Revenue and Benefits of this.
I am arguing that from 24/8/09 - 11/10/09 the tenant should be held responsible for the overpayment . This is due to the fact they failed to notify you of a relevent cahnge incircumstances.
For the period 12/10/09 - 13/12/09 i believe it to be official error as Revenue and Benefits had been informed twice by the DWP and they had failed to act upon the information provided twice !
Any comments would be apreciated. Thanks