Is it permissible for a female student to provide a free explanation of academic material to her classmates, even though the teacher who sold her the explanation at a high price does not permit its dissemination or transfer?

It is permissible for you to benefit from the copy you purchased or to gift it to whomever you wish. However, it is not permissible for you to photocopy it and multiply its copies to distribute them to students as long as its owner prohibits that. These intellectual property rights, such as copyright, may not be infringed upon, and they have a recognized financial value in Islamic law.