If you know how to copy/paste in tmux, you just do it as usual, it doesn't matter left side is vim or other process.
On the left side, you enter tmux's copy-mode (with your shortcut), select lines, do copy (copy to tmux's buffer), switch to right side, paste (with your shortcut). Done.
If you know how to copy/paste in tmux, you just do it as usual, it doesn't matter left side is vim or other process.
On the left side, you enter tmux's copy-mode (with your shortcut), select lines, do copy (copy to tmux's buffer), switch to right side, paste (with your shortcut). Done.