You can repost an Instagram story you’ve been mentioned in, but only if your profile is a public account. Follow these steps:
Open Instagram and tap the messages icon
Select the message history between you and the Instagram user who’s tagged you in their story
Tap “Add this to your story”
You have the option to make any edits; then you tap “Next”
You can choose how you want to post it as well as who gets to see it. You make these decisions via the “Share” or “Send” options