I have a question concerning whether it is permissible to teach, in the form of correction, a non-Jew who has already been exposed to halakha. The correction taking place when they are publicly misquoting or misapplying what they learned from an invalid source. I will need to explain the situation. I once worked with a group of people from the Igbo ethnic group in Nigeria who ?felt? they had Jewish ancestry. I tried to get them to understand that they would need to go through an Orthodox conversion, but at the time they had been influenced by members of the Reconstructionist, Reform, and Conservative movements who were able to actually go to Nigeria and meet with up with the Igbos face to face. There were number of the of the Reconstructionist, Reform, and Conservative Jews who went the Nigeria and misguidedly convinced certain Igbos that Orthodox rabbis would never convert them due to racism. Over the years the Igbos had been provided with tefillin, books on halakha, in some cases Torah scrolls, etc. by said of the Reconstructionist, Reform, and Conservative Jews. Some Igbos, who were outside of Nigeria did convert through an Orthodox Beit Din yet the vast majority of them are not halakhacially Jewish through an Orthodox means. It must be noted that before taking on Judaism most of the Igbos were Christian or even messianic, due to European missionary influence. I recently came across a discussion amongst certain members of this group who were discussing an issue of some Igbos in a picture with a Reform Jew and all of them were wearing Tefillin. One Igbo commented about the picture while misquoting the Shulchan Arukh. I responded by correcting his mis-statement by quoting the relevant sections of the Mishnah Torah and the Shulchan Arukh. I also made it clear that since the men in the picture were not halakhically Jewish, and at most could be considered Noachides, it was not correct for them to wear Tefillin. My concern is that the mis-information they were already provided is causing them to come to some wrong conclusions about Judaism, and even about Orthodox requirements for who is considered a Jew. I have seen this mis-information amongst some Igbos cause a certain dislike towards Orthodoxy due to the influence of those who were able to visit them. So now to my question. Given the above, it is permissible by halakha to correct a non-Jew when they publicly are making a mistake with halakha that they incorrectly learned either on their own (internet) or from an errant Jews?

Of course one should correct a mistake, and it's not considered teaching Torah to a gentile. By all means clarify that we are not missionaries and are not at all interested in converting any (!) gentile, but one who is adamant and sincere, we'll accept no matter what color!