I am not entirely sure if you are referring to stored data within a data store, or the contents of a game universe itself. Regardless, both are possible. Data store sharing is a bit more difficult, but I will summarize what to do.
Just in case, I will explain both, as I am unclear on which you mean.
Place Transfer:
Click File > Save/Publish To Roblox To…
Click the drop down menu and select your group.
Choose which place you wish to transfer the game to.
Make sure it is the correct place, and click “Overwrite.”
Data Store Transfer:
Note: This method uses both DataStoreService and TeleportService. If you are inexperienced in these areas, I recommend reviewing the documentation that I have linked above.
The only time I have ever seen this was in group recruiting plaza, which accomplished it (so I think) as so:
Prompt players with an interface asking if they had data on the old game, and if so, teleport them to the old game.
In the old game, change the code to load their data, and then teleport them back to the other game with the data attached to their “TeleportData” parameter.
Upon arriving into the new game, check if there is any data, and take it as their old data save.
I am not sure how effective this is, nor do I know of any other methods.
Good luck! I hope this helps answer your question.
-- Sorry for receiving a dead thread but I feel like I need to warn anyone in the future looking at this that TeleportData is not secure and can be spoofed by clients, so keep that in mind if you consider handling data transfer this way.