Y.D. (1:157): Question: Concerning a convert who does not accept the obligation of doing mitzvos is he considered a convert? Answer: It is clear and obvious that he is not a convert at all even after the fact. This is also what my father actually ruled in Strabin. He said in such a case that the person was not a ger in any sense whether for leniencies or strictness. That is because the acceptance of mitzvos is an absolutely necessary condition to become a convert (Shulchan Aruch Y.D. 268:3). Even if the person asserts he is accepting the mitzvos – if we are aware that he is not actually accepting them – his assertion is meaningless. While it is true that if a person is converting for the sake of marriage it is valid after the fact – but that is only if he is fully and truly accepting the mitzvos for the sake of marriage. This is clear and obvious. All this was stated explicity by my father when he ruled in this case. I really don’t understand the reason why some rabbis err in this matter. Even according to their mistaken view that the acceptance of mitzvos is not required – what is the benefit that they are providing for the Jewish people in accepting as converts those who don’t accept the mitzvos. It is certain that G‑d does not approve nor is it desirable for the Jewish people that such converts become mixed into the Jewish people. It is simply obvious that such a person is not considered a convert.
Y.D. (1:159): …In general this whole enterprise of conversion for the sake of marriage is displeasing to me. Therefore I refrain from involvement in it. Not only from the halachic viewpoint that one should not convert someone for the sake of marriage lechatchila, but also because of the reason - that it is almost certain based on our experience - that they are not actually accepting the obligation to do mitzvos. They are just making empty assertions that they will keep the mitzvos. The fact is that without the acceptance of doing all the mitzvos – even one detail (Berchoros 30) - that they are not to be accepted. This is not comparable to Shabbos (68) of a person converting in isolation amongst the non-Jewish population and he doesn’t know about Shabbos or the prohibition against idolatry – nevertheless he is considered a genuine convert since he is fully and sincerely accepting all the obligation encumbent on a member of the Jewish people. Such an acceptance is valid since it an acceptance of the entire Torah – even though he does not know what these halachos are. In fact concerning every prospective convert it is not necessary to inform him of all the mitzvos before he converts. After the fact it is not necessary to inform him of anything as is clear in the Rambam and Shulchan Aruch sif 12. However if he in fact is not accepting the obligation to do all the mitzvos he is not accepted as a convert. This is the essence of conversion. However it is a fact that the majority of converts in this land who convert because of marriage – they do not actually accept to do the mitzvos even though they assert they are. It is well known that they are lying. That is because they are not concerned about being more religious than their husbands who are non observant and transgress all the laws of the Torah. However perhaps in the present case that you are asking me about - she will truly accept the obligation of doing mitzvos. Therefore I am not making a ruling about the validity of the present case to you because there are many rabbis in New York who accept this type of convert. Therefore there is no reason for me to say that it is prohibited to accept her. However I personally am not happy with this. My father also did not find it acceptable but did not say it was prohibited to accept such converts. Therefore you should do according to your understanding of the situation and how urgent you perceive it….