Sorry, but you will have to purchase it again unless your can join a Family Sharing group with that other person in the group and the app is one that can be shared.
Set up Family Sharing - Apple Support
From : How to download apps and content that your family members purchased - Apple Support
Use your iPhone or iPad to download content that family members purchased
1. Open the App Store, Apple TV app, or Apple Books.
2. Find your family member's purchases.
◦ App Store: Tap your profile picture at the top of the screen, then tap Purchased.
◦ Apple TV app: Tap the Library tab, then tap Family Sharing.
◦ Apple Books: Tap your profile picture at the top of the screen.
3. Tap your family member's name to see their content. Learn what to do if you don’t see any content or can't tap your family member (click here —> If you can't find your family's shared apps and content - Apple Support ).
4. To download an item, tap the Download button next to it.