Adel, I'm going to stick to the train frame and give some names to things so we can be clear about what we are discussing:

IN THE TRAIN FRAME
A and B are the two ends of the train.
C is the point somewhere between them where there is a light source.
p is the event "a light signal is emitted at C".
q is the event "the light signal from C reaches A".
r is the event "the light signal from C reaches B".

What you seem to be claiming is that it could be possible to send a light signal from A after event q that will reach B before event r. Am I correct?