Twitter first started to test a feature that let you share your tweet on your Instagram stories last December. And now more than 6 months later twitter started to rolling out this tool to share tweets to Instagram stories to all iOS users. Now you can share tweets to Instagram stories without taking screenshots. You can use this feature to share tweets to Instagram stories by tapping the share button, and on the share, menu selects the New Instagram Stories option.
And as for now, you can’t interact with the tweet on the Instagram story, which means that you can’t like or comment to the tweet on Instagram, if you want to interact with it you have to go to the Twitter app.