Move? No.
But: your CMDR is stored at FD and identified by the email you use to login at FD. So, if you do what Arsen Cross advises against in his first bullet point, i.e. link your Steam account to the same FD account as your Epic account, you will only have one CMDR.
You will still have two game installations on your HDD, but they will both use the same bindings and settings, as those are stored elsewhere and under the game's control.
I'll not delve into the cross-platform issue, sticking instead to your original query. I thought that you could simply link your Steam account to the Frontier account that you use to play Elite Dangerous.
If you go searching for Epic posts on these forums, you'll find many of late (obviously). By far the one I found to be most helpful is the one by Arsen Cross (linked below). While it's not directly addressing your situation, I belive that the answer is in there. Look at the first bulleted item in his post under 'Rules for Elite accounts obtained via Epic Games Store'
Epic Games Accounts - Rules & Considerations
Hello everyone! I'll try to keep this straight forward, short and sweet. I've done experimenting with the new Epic Games store and will now share with you some rules and tips so you can avoid wasting your time during account setup. Rules for Elite accounts obtained via Epic Games Store...forums.frontier.co.uk
Yes? No?
Hi, I have the same problem as the OP, can anyone confirm that if I buy the game on steam I can continue my same character?
I don't want an alt and I have no time to grind again.
But what exactly do I have to do now to "transfer" my savegame or whatsoever from Epic to Steam?
You can have both installed (I do, plus Standalone).Short question in addition: Do I have to uninstall the Epic version first before installing the Steam one? Or can I install them both in parallel in theory?