Thank you for your reply.
I must say to all of you reading this post,that I believe I found the problem.
There is nothing wrong with LCPD:FR, neither ELS v8.
Is just that, when LCPD:FR states that is NOT compatible with third party mods, they really mean it.
And by that,I mean, after countless experiments with the way and order I install mods, I figured out that several mods, mainly those who replaces police vehicles and police uniforms,may cause for some reason that I don't know, LCPD:FR to crash.
Some mods can work with LCPD:FR, some others just can't.
Usualy is not your installation of LCPD:FR nor your pc specs, is just that this particular mod we are using at the time, is not friendly with LCPD:FR on certain actions, in my case, when calling for suspect's transfer after an arrest.
So, in conclusion, keep trying and experimenting with different mods, and see which one "fits" you.