How do you save a JPEG that matches Print Overview of a file? So colours look like the final print?

I created a CMYK illustrator file of a food bag design and I've had a process print-ready file back file from the printer's art department which requires changes. 

For several reasons I can't go back to my original file. 

The problem is the bag colours that aren't direct pantones are now in layers (blue and yellow to make green for example) and only look the correct colour in Print Overview view.

That's fine for editing, but when I save out/Export a JPEG for team approval or sharing, the final look of the colours is lost, and it appears with yellow and blue plate colours.

So how do I save out a JPEG/PNG etc of the bag artwork that actually looks like Print Overview version of the bag? 
I searched forums and YouTube and can't find anything?
Thanks