Remove the original toilet paper or towel bar from the wall by removing the setscrew located at the bottom of the plate or the two screws on the top of the plate using a screwdriver. This releases the post from the plate.
Remove the plate from the wall by unscrewing the two screws anchored into the wall using a screwdriver.
Pull out the anchors from the wall with the end of the screwdriver. If the anchors will not come out easily, push them into the wall and let them fall into the space between the walls.
Insert new anchors into the wall, using toggle anchors and a rubber mallet if the fit is tight. The toggle anchors work better than simple straight anchors because the back of the anchor pops out into a T-shape that holds onto the drywall from the inside.
Screw the new plate into the new anchors in the wall using a screwdriver. Attach the new toilet paper or towel holder on the plate.
Remove the original toilet tissue holder from the cabinet wall by removing the setscrew on the post of the toilet paper holder using a screwdriver. This will release the post from the plate.
Unscrew the plate from the cabinet wall using a screwdriver. Hold your hand inside the cabinet to catch the anchors, which will fall when the screws are removed.
Place a 6-inch long, 1-by-4-inch board on the inside of the cabinet over the existing holes. Hold the wood parallel to the top and bottom of the cabinet.
Screw two screws, with washers, into the wood, from the outside of the cabinet at each end, using a cordless drill. Place these screws in between the original holes to hide them during regular use.
Attach the plates to the new toilet tissue holder with 1-inch screws in place of the screws provided with the new toilet paper holder. Two screws hold each plate to the cabinet wall.
Slide the posts into the plates and add a new roll of toilet paper.