Instagram allows you to repost only posts you've been tagged in. So, you can only save and repost stories you've been tagged in. When someone tagged you in a story, they allow you to share that story. But there are still a few things you can do if you want to republish an Instagram story that you're not tagged in. You can either turn on your screen recorder and share it in your story. Or as a simple solution, you can ask your friend to send you that video.