There is no automatic way to propagate a menu into several website.
The only thing that can be done is either create a website with the pre-defined menu that will be later replicated at the creation of other websites.
The other solution consists in using the "Multi Sites Menu Item" that allow accessing menu that are already defined in other websites. Once you have created a menu item, you can change its definition in the other websites and their update will be taken into account by all the Multi Sites Menu Item that reference the menu item.
But this extension will not create the menu item automatically. You will have to create the menu item manually.
See
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