You simply need to make sure that the network user accounts on the frontend / client machines have adequate permissions to use the server machine share folders for the backend. Your system administrator should know how to do that with no problem.
I mean after this splitting is there anything crucial left to do to make the users to work with the application pls
If you have Access security settings on your database you should set permissions on database (back-end) tables. When the tables are re-linked tighter permissions of the database back-end will be effective.
Users must also be allowed to modify the file from the server's permission side, even if they're supposed to only View (Read) records. You block them from editing records through Access, not the server.