Ok, I'll make that an answer.
Disclaimer: I am not a registered terraformer, consult your local registered terraformer before actually performing astroengineering works.
You cannot do. At least, you cannot say: "I will put my electroscientimagic device at point P, push button B at hour H and then I can call it a day".
What your elecroscientimagic device will do will be applying energy. That energy (minus inefficiences) will go into breaking the Moon (which by itself is not a big change) and giving the fragments enough energy to leave the Moon's gravity and get into Earth orbit.
Say you only make two halves and want one of each half in opposite points of the Moon's orbit. For the fragment you move, you need to:
- accelerate to Moon's (well, half-Moon) escape velocity.
- put in the desired point of the orbit.
- accelerate (o deccelerate) to the needed orbital speed to keep that orbit.
Now, by doing that change, you have changed also the center of masses, so you will have to adjust the orbit parameters of both halves of the moon.
To do your project, you will need to begin a long time process that will need constant supervision and readjustments. And of course, you will need some reason that justifies such effort.