Have some update..
I received a PM from forum user (thank you Jean-Pierre) with information that the only timezone setting which gives the correct time for him is Brazzaville GMT+01.00 (Central African time). I tried it and voila I have correct LT on the screen now. But I wanted to find the root of the thing
so I switched back to GMT+1 Central European setting. Nothing changed in FIF, LT is still correct. Then I tried to set so different timezone GMT+3. Still nothing changed in FIF. Tried various settings, closed and restarted the FIF between attempts. Android switched the new time immediately but the FIF kept showing GMT+1. Then I've got an idea to restart the system. Now FIF showed actual Android timezone (GMT+3). Then I set GMT+1 Central European timezone back. Started FIF and the time was correct without system restart this time. Pretty strange behavior.
My Android version is 4.4.4