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Problem: How to set the permission for user to edit the WP menus.?
Solution: Toolset Access has an option under: Access Control >> Custom Roles >> Change permissions option -- see screenshot. https://wp-types.com/wp-content/uploads/2017/09/567232-Change_permissions.png?x62720 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: https://www.thewebtaylor.com/articles/wordpress-allow-editors-to-manage-menus https://wordpress.stackexchange.com/a/10306