Add the following to ~/.tmux.conf
for long buffer support and ability to write to file afterwards:
set-option -g history-limit 250000
bind-key P command-prompt -p 'save history to filename:' -I '~/tmux.history' 'capture-pane -S -250000 ; save-buffer %1 ; delete-buffer'
Type Ctrl+B -> Shift+P then enter filename and hit Enter to save