Transferring your GTA story is often not possible. This is because the game's architecture and save systems are designed to be specific to each version and platform. There may be some exceptions with certain mods or unofficial methods, but these come with risks and might not be supported by the game developers.
As I don't have a GTA story to transfer myself, I can tell you that in general, the main limitation is that the game saves are often device - specific. So, it's hard to transfer from a PC to a console or vice versa. Also, if you try to use unauthorized methods to transfer, like some dodgy mods, you risk getting banned from the game.
In the world of GTA, the story mode progress is tied to your individual game save file on your console or PC. You can't transfer your story in the sense of giving it to another player. However, if you are talking about transferring your story progress from one console to another, for example, from an old Xbox to a new Xbox, there are some official ways for some platforms. For PlayStation, you can use the cloud save feature if you are subscribed to PlayStation Plus. For Xbox, Xbox Live also has a similar cloud save system that might help in migrating your save data which includes your story progress. But this is more about migrating your own data to a new device of yours, not sharing it with others.
Sure, you can transfer money in GTA 5 story mode. This can be achieved by methods like doing heists, side missions, or engaging in business activities within the game world. But keep in mind that there are rules and limitations imposed by the game to maintain balance and challenge.
Sorry, you typically can't transfer your Lunaria Story character to a different server. This is to ensure fairness, stability, and the integrity of the game across all servers.