Strange, on one of my accounts, the folders are replicated, but not the inbox folder.
I do not see mails in inbox in eMclient.
I see them online whe using the interface of my provider (web.de)
When i move a mail from the inbox to a folder, then I see it also in eMclient 
any idea?
As it’s IMAP, you should not lose anything if you just delete the account and set it up again in eM Client. That’s what I would try if there is no obvious solution.
I think I just found the issue 
It’s a combination of a so called “3 ways spam protection” of my provider and the new V8 “more” button (“more” is a feature and not a bug I was explained)
3 ways means incoming mail is split in “friends”, that’s inbox, “unknown” and “junk” directories.
well this “unknown” directory is not recognized by default by eMclient and if you do not take it out of “more”, well you never see it. Not even downloaded it seems.
Similar issue with apple mail on my phone, Directory “unknown” shows there but new messages not appearing in inbox.
stupid but solved by disabling this functionality. 
Well, this solution was hard to guess. Luckily you found it yourself.