This issue has undoubtedly come up before, and your university probably has an explicit policy in place for how to deal with it. For example, Harvard's policy says:
It is the expectation of every course that all work submitted to it will have been done solely for that course. If the same or similar work is to be submitted to any other course, the prior written permission of the instructor must be obtained. If the same or similar work is to be submitted to more than one course during the same term, the prior written permission of all instructors involved must be obtained. A student who submits the same or similar work to more than one course without such prior permission is subject to disciplinary action, and ordinarily will be required to withdraw from the College.
Similarly, Yale's policy says:
Students may not submit the same paper, or substantially the same paper, in more than one course. If topics for two courses coincide, a student must have written permission from both instructors before either combining work on two papers or revising an earlier paper for submission to a new course.
In particular, you should not improvise a response, unless you find out for sure that there is definitely no official policy (strange but possible). If there is a policy, then it will specify what the rules are and how they should be enforced.