Global site search optimization

Hi guys,

Got some issues in here. Actually not issues, but some optimizations.

I'm using "Origami" theme on my main multisite.

Now, I would love to insert simple search form into my menu, but results to be from Global site search plugin.

Already set up plugin Global site search and i need that form, or php shortcode od function to put inside my menu.

If someone can help, i would be more than gratefull.