We have our Product Backlog as a physical Kanban board with TODO & DONE column.
Some of the stories are moving from the TODO column to the Sprint backlog during our planning, and then during the Sprint review back in the Product Backlog in the DONE column for the one which we completed.
I was wondering if keeping history of DONE stories on the wall was intresting at all. It's starting to take up space Sprints after Sprints and I can't see any value from it for now.
You should only have your sprint backlog on the board and not your full product backlog.
I personnaly keep a certain amount of Done stories until I'm out of space, and after that I archived them (if I'm using an electronic board) or put them on each other if I use a physical dashboard.
I use those cards in my hands at the review and retrospective.
Try to go Lean here. If keeping the DONE stories past the completion of a given sprint is taking up space on the wall and not adding any value, it's a waste and it's time to make a process improvement. I'd hesitate to just throw them away until you are sure you don't need them, but I'd consider archiving them, either physically or electronically. That way, if you need to consult or refer to the stories, you have the information. In the future, if you don't use this archive, then you can talk about the next step of getting rid of the archive.