Shut off the valve for the refrigerator water line, turning the knob clockwise until tight. The valve is located either behind the Kenmore or under the sink, where the water line connects to the cold-water pipe.
Pull the Kenmore out from the wall so you can get behind the appliance to access the connections. Unplug the refrigerator power cord.
Open the freezer door and remove any frozen food blocking the upper back wall. Pry off the plate labeled "Icemaker" with a flat-blade screwdriver inserted into the notch at the bottom.
Connect the plug on the end of the icemaker's wire harness to the power socket inside the back wall of your freezer. Ease the wire harness into the space surrounding the socket.
Align the tabs on the icemaker with the notches on the freezer and slide the component downward into position. Attach the icemaker to the freezer with the two supplied screws through the screw holes in the component, which align with the screw holes in the freezer wall.
Turn the water fill tube above the icemaker so that it fits inside the icemaker fill cup.
Wrap plumber's resin-coated tape around the nozzle threads on the back of the refrigerator, on the freezer side near the top. Push the tape into the threading on all sides.
Slide the coupler on the end of the water line over the taped nozzle on the back of the Kenmore. Twist the coupler clockwise with your fingers as far as it will turn, then twist a half turn with pliers to seal the connection.
Turn the water supply valve knob counterclockwise to release water to the Kenmore. Check the back of the refrigerator for any leaks around the connection. Tighten the coupler with pliers, if necessary.
Dry your hands before plugging in the Kenmore power cord to the wall outlet.
Press the toggle switch on the icemaker to the ''On" position and replace any frozen food you removed earlier.