It would be good to be able to share items from the Activity screen to anywhere, but especially to social media platforms.
@TomAsh specifically proposed sharing the free shares with some short information about the platform as a way of getting some free promotion.
This could also be applied to anything in the activity list though, such as just buying or selling. You could customise the messages based on what kind of item they’re sharing. For example, something about how much they bought a share for, or whether they made a profit with a sale, etc.