Is there a way to move windows across screens in task view?

I am using Windows 10 with two screens and making use of the multiple desktops. Despite best intentions of keeping my windows organised, I inevitably end up needing to shift programs between desktops and monitors.

When I press Win+Tab to open the task view, I am able to move applications from one desktop to another but not between monitors. In other words, I can move an application from the left monitor on desktop 1 to the left monitor on desktop 2 but not to the right monitor on desktop 1 or 2.

To organise my desktops I need to:

1. Move each application to the correct desktop
2. Open up each desktop in turn and move applications to the correct screen

Is there a way to move an application between monitors as well as desktops?

My searches have only turned up this unanswered question from last year.

Perhaps I am not understanding accurately what you wish to accomplish, but I believe I do… And I am able to move windows between screens with:

Shift+Win+Left and Shift+Win+Right shortcuts.

This cycles the active window of virtually any application through my monitors based on a number that is assigned internally by Windows to identify each monitor (it usually coincides with the number/order your see in the Screen Resolution control panel). Right moves the window to the higher numbered monitor; Left cycles down to the lower numbered monitor.
This generally coincides with the relative positions of the monitors.
Assuming the monitors are set to the same resolution, the window will maintain its size & position.

Make sure that the checkbox for the setting "Prevent windows from being automatically arranged when moved to the edge of the screen" is NOT checked!
For some reason this setting disables those shortcuts. That setting can be found at:
Control Panel => Ease of Access Center => Make the keyboard easier to use; under the heading "Make it easier to manage windows".

I do not know if there is a native way to move windows/applications between desktops (I don't use multiple desktops), but there is a way as I've seen someone do this (it could be a 3rd party app?).

I find this extremely useful and I use it all the time, literally many times a day!

I do not recall where/when/how I learned about this, but it is not well documented.