Unfortunately, Google does not support this. However, you can link your device to multiple Google accounts, and this should allow you to avoid another purchase.
In the accounts area of your device's settings, establish a link to the Google account your original purchase was under. When setting up the link, make sure to turn on synchronization of app data. Once this is done, you may need to reboot your device or uninstall and reinstall Ultimate To-Do List to ensure the license is detected.