Drop the new light fixture into the pool and extend it out to straighten the attached wire.
Remove the screws holding the junction box's cover in place. Lift the cover off the junction box. Make sure no power is being supplied to the wiring by holding a circuit tester against the wiring. If power is indicated, turn off the power supply from the main breaker box. Insert a fish tape down the opening and through the conduit until it exits the niche's opening.
Wrap the light fixture's wires around the fish tape's hooked end. Reel the fish tape back through the conduit, dragging the light fixture's wires along with it. Pull the wires 5 to 6 inches up, into the junction box.
Strip the wires' ends with wire strippers. Match up the wires from the junction box with the same colored wire from the light fixture. Twist a wire nut over each wire connection. Place the junction box cover over the wires and secure it in place with the screws you removed in step 2.
Coil the excess wire in the pool and put it in the niche. Insert the light fixture into the niche and line up the fixture's tab with the niche's groove. Line up the fixture's screw hole, located at the top, with the niche's screw hole. Secure the light fixture in place with the light fixture's supplied screw.