Unfortunately, Snapchat does not notify users when someone screenshots their Story. The app is used to send notifications when someone takes a screenshot of your snap, but they only notify you if a screenshot is taken of a direct snap, not a Story.
You can check who screenshotted your Snapchat story in the profile settings. There are a few simple steps to view who screenshotted your Snapchat story.
1. Go to your Snapchat profile.
2. Click on the story that you have posted into it.
3. swipe right to check the screenshotted users, who have taken screenshots of your story.
For more easy understanding take reference from the snap below.