Ok, so you have an event structure that handles menu selections, but now you want buttons to launch the same code, right?
If you can make a sub-VI of the code you want to run in both cases I would do that, and then have the sub-VI in both event cases. If not:
To get a button to fire a menu event is not possible as far as I know, but it would be easy to do it the other way around. Put the code in an event or case triggered by the button or a hidden button that you set to true when the menu selection is done (you could use the same button, but that looks a bit strange; the button would go true without anyone clicking it). If you use an event, set the value of the boolean using the value signaling property instead of a local; that way the event will fire.
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hird alternative is to skip the buttons and just add keyboard shortcuts to the menus...but that's not quite the same.