Your saved quotes sync across your devices. Use the same password on each device to share the same set of quotes. Anyone with this password can see these quotes — keep it private.
To move a quote between devices: first open this on the device that already has the quote and tap Connect & sync (that uploads it). Then on the other device, enter the same password and tap Connect & sync to pull it down. Already connected on both? Just tap Connect & sync again to refresh.