Mormon missionaries use this verse to encourage prospective converts to pray about their scripture called the Book of Mormon. They say that those who pray about this book should receive a good feeling from God to show how Mormonism is true. Yet James never intended such a meaning. Rather, he was instructing his readers about trials and maturity. When Christians are in need of wisdom, especially when going through hard times, God provides the requested wisdom. While prayer is definitely important, there are some things that about which prayer is inappropriate. For example, we have not been instructed to pray about possibly stealing a neighbor’s car or disobeying parents. Why not? The scriptures clearly instruct that doing these things would be wrong, regardless of any good feelings generated through prayer. If the Mormon Church were true, this would be evident through its teachings and faithfulness to biblical teachings. If a church does not line up with the truth, the problems should be obvious to the careful observer (Gal 1:8-9; 2 Cor 11:4; 1 John 4:1).
For more information, see “Does the Mormon’s testimony prove the LDS Church is true?” Also see a blog by Sharon Lindbloom.