Hi There!
I have done this many times, and I will sure you that it will be a smooth process and all your developed reports will be fine.
The plan to deliver the new installed Dynamics Management Reporter with the existed reports is as following:
1. Take a backup of Management Reporter databases
2. Take an export of all your developed reports from the existed Management Reporter
3. Uninstall the existed Management Reporter
4. Install a new Management Reporter (Service & Client) with the recommended CU Update for your Dynamics AX 2012 R3
5. Configure the new Management Reporter Service and connect it with the Dynamics AX 2012 R3
6. Configure the new Management Reporter Databases
7. Sync the data between the Dynamics AX 2012 R3 and Management Reporter
8. Import the exported reports "step 2" to the new installed Management Reporter