HB for prisoners on remand and then sentenced.

I am seeking clarification of the rules around prisoners claiming HB.
A prisoner obviously gets HB for up to 52 weeks on remand but as I understood it if they were then sentenced and were likely to be out in less than 13 weeks this was treated as a change of circumstances and treated as absence from home under the 13 week rule.
The Shelter HB book written by John Zebedee seems to confirm this (point 3.39 - page 42) but confusingly the CPAG handbook states that if you are serving a custodial sentence the 13 weeks runs from the date you were first in prison and so any time spent in prison awaiting trial counts towards the 13 weeks (page 657).
I’m a bit baffled because these seem to be two different interpretations of the rules. Under the CPAG determination anyone who spent months on remand but then received a relatively short sentence would not be entitled to HB. Is this correct?

Although the sentance may be relatively short in terms of the release date the actual sentence will include time served on remand.

Thanks, but does the sentencing count as a change of circs? Say, hypothetically, after they have been on remand for 40 weeks and then get a sentence that means they will do another 8 weeks in prison after taking time served into account, can they get HB in prison because they are unlikely to be away from home for more than 13 weeks?

Sadly no, once sentenced the 13 week absence rule applies from the very start of the absence

Curiosity, would the 40 week payment be considered as an overpayment ?