Log in as non-shell user?

I've set up a SSH server with sftp support. It works fine for most accounts, but when I try to log in using an account with /bin/false as shell I get an error. It says: "Cannot initialize SFTP protocol. Is the host running a SFTP server? Connection has been unexpectedly closed. Server sent command exit status 1."
But I'm sure the SFTP server is running.
I really could use some help with this.

Unless you are able to connect with other client, I believe that it is your server configuration issue.

But I'm sure the SFTP server is running.

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From my experience, SFTP server is started only after you connect to server. It is not standalone server, running all the time. It is rather subprocess of SSHD. I do not know how this works, but it is possible that unless user has valid shell, SSHD is not able to start SFTP server for him.