Here’s my take on this.
I can see the challenge here, as stories are designed to be temporary. On one hand, you could try technical workarounds. Some people suggest looking through your phone’s cache on Android, but this is a long shot. The files are often overwritten quickly and can be difficult to access or piece together, making it an unreliable method.
On the other hand, the most straightforward approach is usually the best. The person who posted the story very likely has it saved in their own private Instagram “Archive” if they have that setting enabled. This is a common feature. Reaching out and asking them directly for the content is your most reliable path. Third-party tools generally need to capture a story while it’s still live, so they aren’t much help for one that has already been deleted.