Housing costs

I have a client who was recently widowed. She has severe mental health problems and a mortgage. She has never claimed ESA because she does not have the contribs for cESA and would not have got irESA due to her late husband’s earnings. At present she gets BA and this helps knock her out of entitlement to irESA even with the housing costs. Should she apply for c and irESA 13 weeks before the BA runs out, even though she will get credits only? Would credits only get her treated as entitled to irESA and would the 13 week waiting period be satisfied as soon as the BA runs out? CPAG top of p457 2nd dash and bottom of p457 imply that she would be treated as entitled to and receiving irESA if the only thing preventing payment was income or capital being too high for up to 39 weeks.  But p456 s6 second bullet point says that the modified rules on p453 do not apply if you are treated as receiving irESA during the specified period. p455 para2 says that if the modified rules do not apply, the 26 or 39 week waiting period applies (potentially 39 weeks in this case).  Does this mean that if my client applied now for irESA before her BA ran out she would have to serve a 39 week waiting period starting now? In which case she may be better waiting and applying when the BA stops, and then serving a 13 week waiting period.  Her BA has about 26 weeks to run.