Instagram has long-resisted easily resharing content. While they've been testing a "regram" feature, overall, it lags behind apps such as Twitter and Facebook where resharing is easy. This is probably by design, as Instagram is a bastion of original content, but it has finally opened the doors a bit to let you reshare Stories from those you follow.
This new Stories sharing feature doesn't come without any catches, though. For one, the Story needs to be public (the default). Additionally, you need to be tagged in the Story itself, so even if you and your friend follow each other, you won't be able to reshare their Story unless these parameters are met. All that said, this is still a great feature, as long as you're OK with playing ball.
To tag someone else in a Story, take a picture or video, tap on the screen, then @mention them. You can also tap on the sticker icon and choose the "@mention" sticker to tag someone if you want.
If you want to share someone's Story, you need to be tagged in one first, so make sure your friend does that if you're planning on shipping it out as well. Once they do, you'll receive a notification that your friend tagged you in their Story.
Go to your Direct inbox on Instagram by tapping the paper airplane icon in the top-right corner of the app, then tap the direct message with the person who tagged you. It should be the first one if you were just tagged. There should be a brand new option inside the message: "Add This to Your Story."
Tap "Add This to Your Story," and your friend's story will appear inside a blue border. You can then add a bunch of stickers to it as if it were your own, and add it to your own Story, where it'll stay for 24 hours. When your followers watch your story, they will see the original poster's username tagged at the top of the story, which is tappable.
While this isn't as cool as being able to reshare everything (or even just all Stories), it's definitely a step in the right direction, and it'll probably be widely used by users on Instagram. Because this update is so new, make sure both you and your friends are on Instagram version 48 or higher for iOS and Android.