Can I transfer files between two remote servers with WinSCP?

To transfer files between the two servers via local workstation

See documentation to learn how to duplicate files between sessions.

This feature is not built into WinSCP, for reasons listed further down. Yet, there are ways to utilize some advanced features of WinSCP to achieve

With the SFTP and SCP protocols, you can push the selected remote files to another server using the scp custom command.

With the SFTP and SCP protocols, you can use a suitable remote command to download files to the remote server from another server. E.g.:

wget ftp://username:password@otherhost:/path/file ./

The SFTP protocol does not allow this.
With the SCP protocol it may be theoretically possible. However it has many drawbacks. It would require not only major changes in WinSCP, but also many configuration changes on both servers to allow authentication on the second server from the first one (note that it would not be possible to use an interactive password authentication). See the scp custom command for details. So practically it would have advantage for advanced users only, who can use the “custom command” solution easily.
The FTP protocol has an FXP extension that allows this, but it is disabled on majority of FTP servers. 309