Natively Instagram is a photo and video sharing application. By its nature it is not possible to share Twitter messages on Instagram unless Tweet's photo is taken.
However, Linkzz provides a feature where you can retrieve the Tweet message from its URL and open the message in its advanced design tool.
Tweet URLs are automatically sensed by Linkzz editor and their meta data along with the message itself fetched instantly.
By the help of the design tool retrieved Tweet can be modified;
When satisfied with the result Tweet can be downloaded as photo/image and can be shared on Instagram.
Sharing Tweets on your Linkzz account gives you further power to get detailed analytics over the Twitter message.
This is a PRO feature upgrade to PRO