624. Amira L'Akum
We are not permitted to direct a non-Jew to perform work for us on Shabbos even though they are not required to keep Shabbos. This is so even if the instruction was conveyed before Shabbos and we do not need the fruits of their labor until after Shabbos. This is a rabbinical safeguard to keep people from treating Shabbos lightly and coming to perform acts of labor themselves.
If a non-Jew performs an act of labor on Shabbos on his own accord, if he performed it for a Jew, then Jews are not permitted to benefit from that labor until after Shabbos, waiting long enough that the labor could have been performed on Saturday night. This is the case so long as it is not common knowledge that the act was performed for this person on Shabbos. If the non-Jew performed the labor for himself, it is permitted to benefit from it on Shabbos.