You cannot edit a resource string. If you want to store some string that you can alter programatically you should use a configuration file, or, even better user or app settings (that are actually a wrapper around the configuration file).
The reason that you can't change a resource string at runtime, is because the resource is compiled into your executable. If you reverse engineer the compiled *.exe or *.dll file, you can actually see your string in the code. Editing an already compiled executable file is never a good idea (unless you're trying to hack it), but when you try to do it from the executables code, it just plain impossible, as the file is locked during execution.
You can read more about user settings on MSDN.
You should check out the link, as it contains detailed instructions with screenshots as to how to set your settings through GUI.
In brief, you right click your project->Properties->Settings. Now, you'll see a table where you can add, edit and remove user settings. Once you create a user setting you can use it like this:
//Read
String settingValue = Settings.Default.TestSetting;
//Write
Settings.Default.TestSetting = "newVal";
//Write settings to disk
Settings.Default.Save();
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