I use eM Client on my Mac and mobile phone. On my phone, I also use Aqua Mail. I’ve created several subfolders in Gmail, which are of course enabled for IMAP sync in the Gmail settings. When I manually move emails into one of these subfolders on my Mac, they aren’t reflected in eM Client on my phone. Aqua Mail works perfectly. Manually refreshing the subfolder doesn’t help either. I always have to move these emails manually in eM Client on my phone as well.
If the app is open and it’s not synching the sub folder changes after you move emails to different mail folders, first check the “Synchronisation interval” in the mobile app which syncs the IMAP sub folders as could be “that’s set way too long”.
Go to “Menu / Settings” and click “Advanced Settings” under Other at the bottom.
If your Sync interval is short and the sub folders are still not updating with your moved mail, then could be “it’s still synching other mail folders” and hasn’t got to update that folder yet which you can check via “Menu / Settings / Show Operations”.
Now if nothing is synching in Show Operations “even after the Sync Interval period” and closing and reopening the app makes no difference, then “could be your current app needs updating” or the account might need removing and reading.
So next check you have the latest mobile iOS app 10.4.5267. If you already have the latest app, then suggest if you have an IMAP, Exchange, Office 365 or iCloud acct, to go back to “Menu / Settings” and remove and readd your account.
Also check that you have done the latest iOS update 26.4 if you have a recent iPhone model.