Common damage to the guitar is a broken head or a completely seperated head. This always looks horrible and cause panic in some cases. Don't worry, most broken heads are perfectly fine to repair.
Try in any case to release string tension as soon as possible, or to cut them, to take away the tension on the crack. Try to keep as much as possible loose parts and wood fragments. Don't glue it yourself.
For the best result, the broken wood has to fit as good as possible. The fresher the crack, the better. Also, there nee3ds to be sufficient surface to glue. When that is not the case, the glueing surface can be extended by routing wooden pens in the crack. Usually a broken neck will be repaired with Titebond wood glue. Unfortunately I am not able to do an invisible touchup of the finish, but I can make sure the guitar is well playable without sharp edges or glue leftovers.
De head of the guitar is snapped off but is still attached. The crack runs along the tuner holes of both E strings. Because the head is still attached, this type of crack is in most cases very well to repair.
The wood is cleaned and glued in, untill far to the end of the crack. With two blocks and parallel glue clamps the wood is clamped together. This type of clamps can apply lots of pressure in a controlled way and never get loose. After one night the clamps are released and the wood is cleaned up. The the guitar rests for another night without string tension.
After two nights the joint is cured enough bare string tension. Any leftover unequalness in the neck is sanded and polished. Now the guitar can be played as before.
The head of this Epiphone Les Paul is completely seperated from the neck. Les Paul type of guitars are quite often in the workshop for broken heads. They are heavy and if they fall there is a lot of force on the head because of the angled construction. Often, a Gibson cracks in a nicer waythan Asian made Les Pauls. They can brake from straight to th grain (as if the head is cut off with a saw) to cracks that are as long as half of the neck length.
The head of this Epiphone has insufficient glueing surface. First, the head is glued back without reinforcements. This happens in a setup with a vise where the head is pressed towards the neck.
When the first glueing session is hardened out, wood is cut out, to make slots over the crack.
The slots are filled up with mahogany blocks that fit precisely. The new joint causes much more glueing surface and a much stronger joint. The blocks are pressed in the neck with parallel clamps.
After drying, the mahogany blocks are cut in the shape of the neck. The wood is finished by wood oil.