The I/O (copy) operation between two different shares does not take place efficiently on the remote side. Instead, all data is being transferred via the client. This is by design of the CIFS/SMB protocol. I can think of two workarounds.
SFTP is built-in to SSH in Ubuntu, so you already have it once you have OpenSSH server installed. In Nautilus, you can do this either using the menu or by entering a manual location.
And browse in your file manager as you would using the command-line way as
Command-line way: press Ctrl+L to get a textual location bar. Then use this as the location:
On KDE (Dolphin), it's
Make them one share
If you prefer to stick with CIFS/SMB access, then the only option I see is to make them one share. You can even make it an additional share or have them there just temporarily.
First, make sure they're mounted on a similar level of folders, e.g.
And then just share