If they are both G07's (which it looks like they are) then yes you can switch neckboards. I've done this many times, most recently on a Wizard of Wor who's owner dropped it on it's back (it has a neck hump), cracking the neckboard but miraculously not the neck.
First, discharge your tubes to be safe.
Place both chassis' side-by-side on your workbench (or table/desk/etc.). There are 6 wires going to the neckboard from the main board. There is a thick white wire coming from the focus/brightness controls, and 5 thinner colored wires (white, brown, red, yellow, and black) which coil around pins soldered into the neckboard. I believe the holes are labeled with the wire color, but maybe not. Don't try to uncoil the wires from the pins. Just unsolder the pins themselves. If the holes are not labeled, completely remove the new neckboard from the chassis it is attached to, then transfer pins one at a time from the old neckboard to the same spot on the new one. The large white wire goes into the yoke pin connector. If you look closely, you will see how a small flathead can release the clips on the plastic housing where the wire goes in. This will pull out of the way and allow you to unsolder the wire, and replace with the new wire. Don't forget to snap the plastic back shut. As long as the drive transistors and pots are good, the colors should look fine.
Also, while you have the neckboard off, replace the cap on it. And replace all the caps on your main chassis if you have not and while you have it out.