Bring the water to the boil in a large saucepan. Add salt, pour in the rice and stir. Cover and lower the heat. Cook gently for around 15 minutes. The rice should be cooked but still retain some bite. Pour it into a sieve and stop the cooking by rinsing under cold running water, drain thoroughly and leave to cool.
Wash the fennel. Quarter the bulbs then dice finely. Peel and quarter the apples, remove the pips and chop into very small dice. Sprinkle the fennel and apples with the lime juice.
Arrange the diced fennel and apple in a salad bowl, along with the rice.