How to install Pro version and do not lose changes made by free version

In case you have a free version of User Role Editor installed:
Pro version includes its own copy of a free version (or the core of a User Role Editor). So you should deactivate free version and can remove it before installing of a Pro version.
The only thing that you should remember is that both versions (free and Pro) use the same place to store their settings data.
So if you delete free version via WordPress Plugins Delete link, plugin will delete automatically its settings data. Changes made to the roles will stay unchanged.
You will have to configure lost part of the settings at the User Role Editor Pro Settings page again after that.
Right decision in this case is to delete free version folder (user-role-editor) after deactivation via FTP, not via WordPress.