Who is responsible for updating the user stories and entering efforts? PO or Scrum Master?

Hello my friends,

I have a scenario to present in front of you as a Scrum Master and patiently waiting to hear your valuable suggestions on this :)

1. PO created the product backlogs with Description and Acceptance Criteria.

2. During the grooming meeting, who will share the screen with the whole team and change the stories based on the team discussions? 

    We enter Efforts during the grooming for the story as a whole which will include development, testing and design efforts. (Is that really required or the effort estimation in planning is enough?)