We suggest using the portrait post size when sharing to an Instagram Story. To select the portrait post size, tap the "+" button on the home screen to open the "Create a Post" screen to start a post. Under "post sizes" you can select the portrait shape. For more information, check out this tutorial video.
Since the posting process is a little different with Instagram, after Instagram has launched, select the camera icon in the upper right corner of the Instagram app to share your story.