Technically you can not make this switch on the same reservation. People are not supposed to book and then have someone else come in their stead. That said, it happens all the time. Sometimes people are up front (someone booking for their parents who might not have an Airbnb account, for example), sometimes not. If you accept this person, and anything happens, you are not protected by Airbnb's policies.
I would recomend having the person cancel, and letting them know that you will be happy to have the other person book the same dates at the same prices using their own account (make sure you get the name).