I'm PO and new to the company.
I'm used to identify and than write down the "pain" of our customer in backlog items (User Stories). Thats my preperation for the refinement where we are than discussing together with the development team, solutions and acceptans criterias of the stories. The actually completing of writing the User Stories during the refinement is done by somebody of the development team. Advantage in my opinion: Developers get a better understanding through writing and understanding and I can focus on explaining the pain and discussing solution with the team.