UPDATE FROM 2021!
Starting from version 2021.1, you can just press Ctrl/Cmd+C on the data source, and then Ctrl/Cmd+V it in another IDE. The clipboard contains XML for the data source, so you can send it to the colleague via e-mail, messenger etc.
It is possible!
You need to share a project with your friend — all you do in DataGrip is in the context of a project. If you did not create a new one, everything is under the default project. Look at the gif:
The more detailed information can be found in the tutorial: https://blog.jetbrains.com/datagrip/2018/05/21/copy-and-share-data-sources-in-datagrip/