The case in this teshuva is of a non-Jewish woman who was married to a Jewish man for 17 years. She lived as a Jew and their adopted children were converted and raised as Jews. She had asked to be converted in the past and had been pushed aside by the previous Rabbis of her community. Now, the new Rabbi asked Rav Moshe Feinstein if he should convert her.
Rav Moshe answered that since all evidence pointed to her sincerity to convert, she should be allowed to do so. However, since her husband was not particularly observant, she would have to be told about הלכות נדה and Shabbat and accept to keep those areas of halacha.
With regard to her having to separate from her husband for three months after conversion (the normal waiting period for a remarriage, instituted to ensure that the woman is not pregnant from the previous husband - in the case of conversion the waiting period is to separate between halachically unacceptable and halachically acceptable conversion), the issue was raised that the woman had never conceived and was now over 40 years old and thus perhaps the waiting period could be waived. Rav Moshe rejected this waiver on the grounds that since the waiting period applied when there had been no previous sin, it would not make sense to waive it for a couple that had lived in sin (intermarriage) for 17 years (לא יהא חוטא נשכר).