Cloning a mushroom is a very good way to preserve the genetic blueprint of that same mushroom. You can clone a mushroom by making a so-called "tissue culture". Tissue cultures are made with the help of agar media. A little bit of flesh from the inside of the mushroom has to be placed on agar media in a Petri dish. Around this tissue from the mushroom will develop mycelium. This mycelium will have the same genetic pattern as the mother mushroom.
A tissue culture has to be made within 48 (but preferably 24) hours after the mushroom has been harvested.
Basically, you can take tissue from any part of the mushroom. But the tissue must be taken from the inside of the mushroom, for this part is practically sterile.
You can extract a part of tissue by breaking the stem or the hat in 2. Use a sterile knife or scalpel to remove a part of the mushroom's inside. A part of 2 by 2 mm is enough. Never touch the outside of the mushroom with the knife, the outside is not sterile and contact with it will most certainly lead to contamination.
Place this piece of tissue in a petri dish with agar as quickly as possible. The risk of contaminating is very large with this method. The chance of succeeding will be larger if you inoculate a number of dishes with a part of tissue.
It could be possible that there is a necessity for selecting a stronger sector of mycelium and taking it to a new dish for further growth.