I've done thorough research on this, and though it's always possible to miss something, I can find nothing specific on whether a mobile-originated custom sort order will sync back to the desktop source collection. Anybody have direct experience with this, or a pointer to some clarifying info? My per-image edits are syncing, so I know communication is happening. I don't know if there's a hidden menu item or checkbox of some kind that I'm missing. Both mobile and desktop are in "custom order" mode. Maybe it's a one-way street?
I have the same problem. Exactly as OP describes :
edits sync, and both desktop and mobile are set to custom sort, yet changing the order on the mobile lightroom app does not affect the order of photos in the desktop lightroom app.
Any super users or Adobe specialists care to weigh in on this?
These threads might help you as the similar info has been shared:
Let me know if that helps!