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How to set the permission for user to edit the WP menus.?
Toolset Access has an option under:
Access Control >> Custom Roles >> Change permissions option -- see screenshot.
If you want more control on Appearance / Menus section, you can use this plugin which offers further control: https://wordpress.org/plugins/adminimize/
Otherwise the custom code solution might work to allow specific user role to manage Menus only, these code snippets might be of your interest: