In case you like someone else’s Highlights and want to download them to your phone, Instagram doesn’t provide a native download button. But there is always a way.
Although no app exists currently that would let you download others' stories, we found a website that does the job – on PC and mobile both. It’s simple to use and lets you download all your Highlights in one go.

Here are the steps:
Step 1: Open the Zasasa website in any browser on your phone or PC.
Step 2: In the text box, type the full Instagram profile link of the user whose Highlights you want to save. For instance, if you want to download Highlights from @ttechbay, type https://www.instagram.com/ttechbay and hit the Download button.

Step 3: The website will load all the Highlights from that profile. If you are using a desktop, right-click the photo that you want to download and save it. On mobile phones, hold the photo and download the image. Repeat the step for all the images that you want to download.

In case you want to download all the images at once, you can do that too. However, this method will work on desktop/laptop only. To do so, you will need to download a Chrome extension that goes by the name Image Downloader.
http://www.ttechbay.com/2018/06/10/how-to-download-someone-elses-instagram-highlights/