Truly directly can be only done if you can run rclone (or filezilla or anything) on one of the servers (A or B). Otherwise all files have to travel to machine C where you run your copier software.
However, using rclone you do not have to download all content of A to machine C first. Transfer can happen "on the fly" without using any disk space (but some small buffers/caches depending on protocol used).
What you need is both A and B support some access method rclone understands (does not have to be the same). Then simply you can run: