I live in Iceland so the don't be alarmed by the late timing of my checkerboarding!

Some data:
I checkerboarded in mid May my two hives which overwintered on two broodboxes and single feedboxes. I only checkerboarded the feed boxes.

My questions:
When should one place a new super on top? Is it immediately after checkerboarding or should one wait for eggs and honey (as I am witnessing now in the top box)?

Do you manipulate the old sugar feed frames later or leave them? I marked them to avoid contamination.

Best regards,