Typically, yes. Public reels are there for others to engage with and share. However, you should still be aware of the platform's rules. Some platforms might have limitations on how often you can share or if there are any additional requirements for sharing certain types of public reels.
Most platforms do permit sharing public reels to your story. This is part of the social sharing aspect of these platforms. But remember, even though it's a public reel, there could be some unspoken rules or community norms. For example, if it's a reel from a particular community that has its own sharing etiquette, it's best to follow that. Also, always respect the creator's work and if possible, give them credit when you share their public reel to your story.