I have this weird acoustic guitar, it's a Mark II... and I wanted to remove the machine heads off it and place it onto my Ibanez.

Is that possible?

The back of the machine head has one screw, and when I unscrewed it nothing happened.
It's as if it's wedged permanently.

Is there any way to replace it?
Daffodils for Delilah.
Acoustic EP.
That little screw on the back does nothing but keeping the knob protruding from a fixed angle neatly in line with the others. Really keeping it in place is either a threaded bush or a flat nut underneath the post. Sometimes you'll have to remove the post first by taking out a screw that goes through the center of the post axle.
But there is a twitch. Tuners come in shapes and sizes, determining how wide the hole trough the headstock should be and how far from the edge and how thick the wood of the headstock should be. You'll need a fair amount of lucky coincidence to be able to swap them just like that.