What is the ruling on teaching or instructing a double-edged matter that can be used in what pleases Allah and what displeases Him, and would a person be a partner in sin if someone else uses this matter in what displeases Allah, even though the matter could be used in what is permissible or impermissible?

Do not teach this matter to someone who will use it for unlawful purposes, unless you know they will use it for permissible purposes, in which case there is no harm. If you are unsure about the matter, strive to be as cautious as possible. There is no sin upon you, Allah willing, if your assumption proves incorrect.