Citizenship applications that lacked POP from 2022 were declined (sort of). This guy who applied in 2019 and was made to reapply in 2022 (apparently the main application form was missing from his file) has had his application languishing in the long queue. When he talks to people at call centre, they say that the processing of his application will continue when he brings POP. He is still waiting for POP from vfs. But this time the application was not returned to the office of application.
Your mom has to wait for her POP. No DHA office will take her application without POP.
In 2019, l applied for verification of PR from DHA office. After 3 years of endless waiting, I applied for POP at vfs in 2022. At the time the official who took my finger prints didn't advise me of the vfs alternative. When I went back to that DHA office in 2024, I found him pleading with a lady to consider applying from vfs. That he couldn't put a time limit on the waiting period of their own 'verification of PR'. Adding that 'it can take 5, 10 years, ... I don't know'. And then he asked me to explain to her about my painful experience.
Dual citizenship letter will be required at the time of filling the citizenship application forms. There was no need to tell her that at the 'verification of PR' stage. If she doesn't get a positive outcome of that verification, then there's no need to have that dual citizenship letter by someone who has not qualified to apply for citizenship.