How to move all windows to another display in Windows 10 quickly?

I use Windows 10 mostly with two displays:

1. The integrated monitor of my laptop.
2. An external HDMI monitor, this is what I mostly use.

Sometimes (particularly after the plug in / out of the external HDMI) most windows move to (1).

Does some quick way exist, most ideally a keyboard shortcut, to move all Windows from (1) to (2)?

Also some script-based solution would be okay, if such a shortcut does not exist.

Windows does not have such a shortcut, so third-party software is required.

This requires some testing, but MultiMonitorTool could be useful. My idea is based on the fact that when a monitor is turned off, all its windows are moved to another monitor.

Here is how to test the idea:

• Start MultiMonitorTool on one monitor
• Use its user interface to turn of the other monitor
• See if the windows on the first monitor have moved to the second one.

If the windows did move then my idea is working, and you could use a script similar to the following to move back the windows:

\path\MultiMonitorTool /disable 1
timeout /t 5 >nul
\path\MultiMonitorTool /enable 1