Place beans and wheat berries in a fine mesh sieve, rinse and drain. Place in pressure cooker with the 4 cups water. Lock the lid in place and close the seal valve. Press the Manual button for 25 minutes. When the cook time ends, use a quick pressure release.
Meanwhile, combine the tomatoes, peppers, cilantro, vinegar, oil, garlic and salt, in a large bowl and set aside.
When valve drops, carefully remove lid, drain in a fine mesh colander and run under cold water to cool completely. drain well. Add the wheat berry mixture, avocado and cheese to the tomato mixture; toss gently until well coated. Serve as is or over leafy greens such as kale.