Spread out newspaper over the area where you will be working. If repotting a tall cactus, the paper should cover an area big enough to lay the entire cactus horizontally and still be on the paper. You can also do this project outdoors to avoid messing up your home.
Wrap the foam rubber or a thick blanket around the cactus. Do this gently to avoid breaking any pieces off your plant. Secure the foam or the blanket with the twine. Tie the twine tight enough to hold the foam or the blanket in place, but not so tight that you harm the cactus
Move the cactus to the newspaper, and gently lay the cactus on its side. Have a friend help you if the cactus is very large or heavy. Working carefully to avoid damaging the roots, ease the old pot off the cactus.
Place 2 inches of cactus potting mix in the bottom of the new container. Lift the cactus and place it in the center of the pot. If needed, have someone help with this. Fill in the sides of the pot with more potting mix, and then place a half-inch layer of potting mix across the surface.
Move the cactus back to its spot in your home. Remove the foam rubber or blanket. Wait until the following day to water the cactus. Water just enough to moisten the soil, not soak it.