To achieve the goal of separating the charges on the two conducting spheres, the student should induce charge separation by using a charged rod.
Given the desired configuration, where one sphere becomes negatively charged and the other positively charged, the appropriate action is to use a positively charged rod. When a positively charged rod is brought near the left sphere, it will attract electrons from that sphere towards the rod, leaving the left sphere with a net positive charge and inducing a negative charge on the right sphere by repulsion.
Therefore, the correct answer is:
B. She should place a positively charged rod near the left sphere.