Shalom, Are there poskim that would allow the recognition of some Conservative conversions? I am aware of the Teshuvah of HaRav Moshe Feinstein zt"l and his statement that a Conservative conversion is not accepted, but are there any who would recognize them if they were conducted properly?

ב"ה Shalom This is a very serious question, with far reaching consequences which must be discussed in your local Bet Din and the answer cannot rely upon a website alone. Moreover, each conversion must be dealt with as an individual case and what may be true in one case may not apply in another. Nonetheless, it is important to clarify here the issue for you and others as well. Conversion means that someone is accepted into the Jewish people. If a conversion does not follow the parameters of Halacha, it means a non –Jew was accepted into the Jewish people with all its ramifications. Therefore, when a prominent Torah authority, such as Rabbi Feinstein z"l , makes such a ruling, it cannot be looked upon lightly. In addition, this is not just the opinion of Rabbi Feinstein z"l. (See Also שו"ת אחיעזר ג כו, שבה"ל י רכז. משנה הלכות יב קצג,שו"ת ציץ אליעזר כא מד.) However, even if wanted for a moment to look for a leniency, allowing someone to become a Jew, is not like finding a leniency to eat some meat which may have had some milk spill unto it. In the case of food in a private kitchen, it may be that one Rabbi will say it's fine and another Rabbi may be more stringent, but the person who asked the Rabbi acted accordingly even if he was more lenient. However, when it comes to declaring someone a Jew, we want this person to be recognized by all Rabbis as a Jew and not a situation, in which in some communities, he is accepted and in some not. Furthermore, the implications are not just for one generation. Therefore, we must act with the utmost caution. All the best