Unless I'm missing something, currently there does not appear to be a way to promote a non-saved window to a saved window. A user must be click the '+' button in the window menu dropdown, then re-open all open tabs in the current window in the new saved window. That doesn't sound fun if one has multiple tabs open.
This would be ameliorated if it was possible move tabs to saved windows without physical drag and drop but that doesn't seem possible as well, see User should be able to move tabs from visible window to non-visible saved windows