When I change note’s enharmony on conductor’s score (working on the instrument’s staff) , that does note affect the instrument part whick keeps the previous note.
I’ve tried the option local/Global but I did not see any change.
Normally, I think respelling propagates automatically from Score to Part, but not the opposite way.
Anyway, you can do this: open the layout containing the note spellings you want to copy, select the notes you want to respell, then Write > Respell > Propagate Note Spellings