Hello Erdinc,
I have observed 2 issues with your mainflow:
1. Un-necessary Movydetail screen.
2. No connection between MovieDetail screen and PersonDetail screen.
Your flow should look like below :

For first issue you have to remove references first and then you can delete the screen
For second issue, you need to make sure your Cast and Crew should have proper link like below :

Perhaps, I don't think it will solve your main issue as AddMovieParticipant does not depend on MovieDetail screen data. Kindly ensure below functionality :
In AddMovieParticipant screen :


Save button screen action flow in core module :

Hope it solves your issue!
Sanjay