All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
What you mentioned, that a woman is allowed to delay her Ghusl until the time of the next prayer is not correct; rather, it is obligatory for a woman, if she becomes pure at the time of any prayer, that she hastens to perform the Ghusl before the time for that prayer ends so that she performs it on time.
If this prayer is a prayer that can be combined with the previous prayer, then she has to hasten to perform Ghusl and pray both prayers.
For example, if a woman becomes pure at the beginning time of the ‘Asr prayer, it is not permissible for her to delay the Ghusl until the time of the Maghrib, and it is not permissible for her to delay it until the ending time of the ‘Asr, resulting in missing the ‘Asr or performing part of it after the time of the Maghrib has started. Rather, she has to perform Ghusl before the time of the ‘Asr ends and pray the Thuhr and the ‘Asr, according to the view of the majority of the scholars.
If she becomes pure at the ending time of the ‘Asr, she should perform Ghusl and pray both the Thuhr and the ‘Asr, even if its time has expired. She is not sinful in this case as she did not intentionally leave the prayer until its time expired.
However, if she became pure at the beginning time of the prayer and deliberately delayed the Ghusl until the time expired, or if she performed the prayer or part of it after its time elapsed, then she is sinful and must repent to Allah.
If the time of the ‘Asr expires before she performs Ghusl because she was negligent or so, then she must pray the Thuhr and ‘Asr before she prays the Maghrib in order to observe the sequence order. The majority of the scholars are of the view that the sequence is to perform the missed prayer first, and then the current one, contrary to the view of the Shaafi'i School of Fiqh (who hold that the current prayer should be performed first).
So in order to be on the safe side, it is better to observe the sequence in order to avoid the difference of opinion.
Allah knows best.