The enzyme that catalyzes the interconversion of glucose-1-phosphate and glucose-6-phosphate is

mutase

Explanation:

A mutase is an enzyme  that catalyzes the movement of a functional group from one position to another within the same molecule, in this case glucose.

The reaction of interconversion of glucose-1-phosphate and glucose-6-phosphate occurs in glycolysis.

Glycolysis is the process  in which glucose is broken down to pyruvate in order to produce energy. It occurs in cytosol and it can be divided into two phases: phase that requires energy (two ATP molecules are used)  and phase that produces energy (four ATP molecules together with two NADH are produced).