I have expiriencing this problem for rather long time: Shift + F6 in midnight commander under screen behaves like F8 (delete file). Google have rather small amount information about this, so I have to use it as it is.
But fortunately i found a solution: when using screen, environment variable TERM is set to "screen". So, we just need to set it back to "xterm" or whatever worked on your host machine. And viola, shift + f6 works as needed.