Thanks for the question. I just had a tenant move from one of my properties to another so I'm probably going to run into the same situation when I try to re-enter him.
From C. D. Bales:" ... I'm probably going to run into the same situation when I try to re-enter him".
You should not have the same problem.
When the tenant moves out of the current property, Edit the tenant, change the "Property", the rent amount (if necessary), and enter the correct new values on the "Terms and Agreement" tab.
Also, at a minimum, delete the rent Reminder for the original property for the tenant.