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.
Launch the Snapchat app on your phone.
Tap your Bitmoji (or profile icon) in the top-left corner.
Under the "My Story" section, tap on your story
Swipe up on your story to see who has viewed it.
If someone screenshotted your story, you'll see a small screenshot icon (two overlapping arrows) next to their name.
Scroll through the list of viewers.
The ones with the screenshot icon are the people who took a screenshot of your story.
Yes, you can view users who take screenshots from your Snapchat Stories by opening your Story followed by a swipe up then a check of the viewer list. The screenshot icon featuring two overlapping arrows indicates an action of screenshot-taking next to any displayed user name.