One way is if they bring up your stories at appropriate times. For example, if you had a great story about a concert you went to, and during a conversation about music, they mention it. Another sign is if they share your stories with others in a positive way, like when introducing you to new people. It shows they value your experiences.
If a friend really knows your best stories, they will be able to add details to the stories when they talk about them. They might remember the little things like the color of the dress you wore at a special event in your story, or the exact words someone said. This shows they have truly listened and internalized your stories. Moreover, they can connect different stories of yours and see the overall growth or pattern in your life based on those stories.
You can tell when they start conversations related to your best stories. Say you had an amazing adventure once. If a friend often asks about it or reminisces with you about that adventure, they probably know your best stories well. Also, if they use your stories as examples to encourage you in difficult times. For instance, if you were down about a job interview and they reminded you of a time you overcame a similar challenge in one of your best stories.