Scrum Board Confusion with Product Backlog Item Column

Question

I am doing an assignment on Scrum. But I am not sure whether my scrum board is correct or not. Here is my scrum table during the first week of sprint:

Here is my scrum table during the second and final week of sprint: 

At the end of the second week, all of my tasks are finished. That's why, there's no item in "To Do" and "In Progress" column.

Now here is the confusing part. Do I have to move all the items from the column entitled Product Backlog Item? Or they will stay just like they are now in the table? I mean, am I supposed to move the things of Product Backlog Items column to Done column?

Hope this helps!

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Thanks!