The problem of adaptation of migrants in receiving countries determines the urgent need to find ways to solve it. The article notes that a special role in the process of rooting foreign citizens in a new community plays the study and perception of its history, traditions, language, spiritual values. Particular attention is paid to the development of tests as one of the means of testing the acquired knowledge, and the socio-cultural adaptation. The authors analyze the materials of the manuals and the content of the exam, enabling foreign citizens to study the main events of history, to get to know the host society. Attention is also drawn to the fact that the increase of the cultural level and adaptive abilities of foreigners in the course of training is designed to improve their image in the perception of Russian society, and reduce the potential for conflict, mitigate the existing social tension in connection with the growth of the migration wave in Russia. One of the evidences of the need to find ways to solve integration problems is the growing contradictions between migrants and their host society in a number of Western European countries. In connection with the active migration policy of the Russian Federation, its desire to create legal conditions for the process of integration of foreign citizens, there is a reform of the migration legislation of the Russian Federation, which leads, in turn, to the modernization of textbooks and control and measuring materials (KIMS) on the module «History of Russia» to a comprehensive exam for foreign citizens wishing to obtain a residence permit. It is noted that preparation for the test tasks of this category of foreign citizens requires a more in-depth study of the subject in comparison with migrants applying for a work permit or patent. The article analyzes the content of materials of textbooks and test tasks, the study and understanding of which will allow foreign citizens not only to gain new knowledge, pass examination tests and obtain a residence permit in Russia, but also in the future to identify themselves with the host society. It seems that the consideration of the process of training of foreign citizens as a means of their integration in the receiving countries is extremely important for modern European society.