Place the beans and wheat berries in a fine mesh sieve; rinse and drain. Place in the Instant Pot with the water. Seal the lid, close the valve, and set the Manual/Pressure Cook button to 25 minutes.
Use a quick pressure release. Meanwhile, combine the tomatoes, peppers, cilantro, vinegar, oil, garlic, and salt in a large bowl and set aside.
When the valve drops, carefully remove the lid. Drain the beans and wheat berries in a fine mesh sieve. Run under cold water to stop the cooking process and cool quickly. Drain well.
Combine the drained bean mixture, avocado, and cheese with the tomato mixture. Toss gently until well coated and serve.