Configure fcitx input method and keyboard layout
Solution 1:
Go to the Addon Config of the Input Method settings, select Show Advanced Options. Then find the X Keyboard Integration, and press the Settings button on the right of the corresponding line. On the popup window unselect the first line: "Allow to rewrite system XKB setup" (or something line this: I look the Russian version). Confirm changes, restart Fcitx. Finally start XKB setting, change something forth and back, and confirm changes (it is necessary to remove all changes in the XKB configuration made by Fcitx). That is all.