'Flagged' folders for separate accounts

I have two inboxes, and the Smart Folder “Flagged” has ALL my “starred” emails. I liked it when I had my Starred folder for each email account IN the email account.  Is there a Flagged for each inbox?

Note: This conversation was created from a reply on: GMail Starred folder dissapeared after update.

could you please go to Gmail webmail and open Settings>Labels? Screenshot the system labels for me.

Thank you.