InStore

Downloaded over 10 million times, InStore is currently the most popular app for downloading Instagram stories. It will save the stories to your phone

Video Downloader for Instagram, Story saver

This app is smaller than InStore and has a better rating.Video Downloader features a textbox where you must paste the copied Instagram story link/URL.

Insta Downloader

Insta Downloader is a great app to save Instagram stories on your phone. It downloads and displays the entire post (text, video, image, etc.).

fastsave

FastSave is a browser app with built-in Instagram, Twitter, Vimeo, DailyMotion downloader utility. Open any social media site and download photo or video

Reels Downloader

Reels Downloader is designed to download Instagram reels and save WhatsApp status on phone, it supports all types of files

Insget

Inset is the only application on this list that enables users to choose download image quality and clear download history. This app doesn't have textbox and lots of ads.

Story Saver for Instagram

The applications will display a popup to log in to your Instagram account if you try to download a story.