tmux

First exit all tmux sessions. Then create ~/.tmux.conf and add these lines to have VIM-like shortcuts to change panes:

bind h select-pane -L
bind j select-pane -D
bind k select-pane -U
bind l select-pane -R

Using tmux in multiple monitors

You can connect to the same session but it acts as a mirror. A better approach is to group sessions. Run the first command in left monitor and the other on the right one:

tmux new -s left_monitor
tmux new -t left_monitor -s right_monitor

Now you have two different sessions (in this case left_monitor and right_monitor) that shares windows together.