I would like to have local copy of inbox (imap server) on my computer.
But I cannot find any local folder "inbox". When I tried to make it manually,
kmail refuses to do, because it already exists!
Is there any workaround? Please help.
System: modern Debian. Kmail version: 1.13.7

If you are using "Disconnected mode" (< 4.14) or "Store messages offline" (4.14+) the messages are saved also on disk when using IMAP. Or do you want a local copy in a separate folder?

I would suggest copying messages to a separate folder in your local folders hierarchy. If you want to make things more automated, perhaps look into the "offlineimap" program and have KMail point at the place where it downloads mails.