Solved HDMI Monitor

Hello!
I have a problem with a monitor, I am hoping someone can solve.
I have a number of monitors connected to a PC, but they all serve different purposes. I only have one switched on at a time.
They use DP connections, so I just choose the monitor I want, turn it on, and Windows automatically adjusts itself to that monitor. It limits the cursor to the display that is on, and adjusts every window to the "on" display.
My problem comes in because I have just added an HDMI monitor.
Windows does not treat HDMI monitors the same as DP. When I switch the monitor off, Windows still thinks it is there. This causes problems because any open windows on that monitor are not relocated to the "on" monitor and the cursor is not bound within the borders of the "on" monitor.
Does anyone know of a solution to this, other than buying a different monitor (one that has a DP input)?
Could I, for example, use some third party dual screen software or perhaps a DP to HDMI cable?

Oh, I found the solution myself.

Windows has a setting "Duplicate" "Extend" "Show only on 1" "Show only on 2" for each window. It remembers the settings for each monitor.

So you can independently configure what happens on the DP monitors. It happens that what I wanted was a setting of "Show only on 1" for the second DP monitor. When that monitor was on and the others were off, it constrains the mouse to the screen and moves any open windows to that screen.