Rules not syncing

When I create a new rule for message forwarding to a folder. This rule is not added in my email provider too. Why? 

Rules created in eM Client are only on the local client-- they do not replicate to the server.  I use gmail and generally I implement rules only on the web app.  This way they process regardless of the 3rd party client you use and don’t need to be reentered if you have to reinstall the client.

I was thinking that maybe you mean that when a rule is implemented in eM Client, the RESULT of the rule is not being synced to the server.  If you are using IMAP, it should replicate the results on the server.  You can click on the “Refresh” button to force this.  If the account is POP3, it will NOT replicate to the server as all POP3 does is download new mails to the local inbox.

Yes, I using the IMAP protocol, but when i create rule in eM client it doesn ̈t synchronize to my email. 

Do you mean the rule itself does not synchronize or the results of the rule don’t?

Rule itself

Yeah, as I wrote above rules themselves will not sync to the server.  I suggest creating the rules on the server using your webmail app.