As far as I can tell the pensioner has to prove that they satisfied the conditions for HB/CTB continuously from the date of claim to the date the claim was actually received.
Circular A29 says “the prescribed time for claiming HB/CTB for a person who has attained the qualifying age for State Pension Credit (the qualifying age), is the day the person is entitled to HB/CTB (apart from the condition of making a claim at the time the entitlement arose) and a period of 12 months thereafter”.
By not responding to your intervention and delaying their re-claim by 4 months I would suggest that the customer has not satisfied the condition of making a claim at the time the entitlement arose, and so cannot prove they coninuously meet the conditions.
As a result I would be tempted to only pay from the 08 November (Monday following date received). However, I’m not certain about this and would probably seek further guidance from the DWP before deciding.