1. Place the wheat berries in a colander and rinse them under cold running water. Drain the wheat berries and transfer them to a bowl. Add cold water to cover by 2 inches, and set it aside to soak overnight.
2. Drain the wheat berries in a colander and rinse them well under cold running water. Transfer them to a large pot and add water to cover by 3 inches. Bring to a boil. Then reduce the heat and simmer, partially covered, until the wheat berries begin to soften, about 15 minutes.
3. Add the salt and cook, uncovered, until the wheat berries are tender, about 45 minutes; test them occasionally while they are cooking. Drain in a colander, and rinse thoroughly under cold running water. Drain the wheat berries well and spread them out on a baking sheet; let them dry for about 45 minutes.
4. Quarter the cucumber lengthwise (do not peel it) and thinly slice the quarters. You should have 1 cup cucumber pieces.
5. Place the wheat berries in a bowl and add the cucumbers, pineapple, and cranberries. Toss well with a fork. Toss in the radicchio and parsley. Add the oil, lemon juice, and salt and pepper, and fluff well with the fork. Let rest at room temperature for 20 minutes before serving.