You seem to have two options.
Option 1: you do not believe the claimant when she says that her son moved out in September; indeed you strongly suspect he has not moved at all. If so, there has only been one change of circumstance so you would make a superseding decision increasing the non-dep deduction from late September and there has been an overpayment.
Option 2: you do believe that the son moved out without leaving a forwarding address, and coincidentally found work the following week. The first change of circumstance is advantageous presumably: £7.40 deduction no longer applies after he moved out. Because this change was reported late, you treat it as if it happened in November. Does this mean that you have to increase the non-dep deduction for the period between the date he started work and the date on which you now pretend he moved out under Reg 8(3)? I don’t think so. Reg 8(3) is a deeming provision intended to deprive the claimant of arrears when they delay reporting an advantageous change. A deeming fiction should only be applied to achieve its intended purpose. When it comes to the change in the non-dep’s financial circumstances the week after he moved out, you would be taking the deeming fiction too far if you pretended that he was still living there. The correct approach is to say that there has only been one relevant change of circs – he moved out. Because that change of circs is advantageous and was reported late, you delay it until November, but forget about that fact that in real life he had started work by then.