That`s ok Janusz.
As I said, this is not related to the browser nor the OS.
The message in the java console gave a good indication of the problem:
URL http://xxxxxxxxxx.com/rimqfa from frame with URL
Domains, protocols and ports must match."
Therefore, as said: "...ports must match...", and at least in this specific situation, it was not the case.
To confirm this, I tried this morning in a situation where the same port was used (everything else being the same: OS, browser) and it works fine.
This situation happens because I'm testing FA in a house internet environment, using DynDNS and I have to use a port different of the usual "80", that one being blocked by my ISP.
I'm just surprise because it is the very first time this happens, and I did a lot of testing with a lot of softwares with this environment.
I will try to solve that temporary (and somewhere false) problem. You could still help by telling me if a part of the URL ("http://xxxxxxx.com/RIMQFA" as an example) is stored somewhere in the files or in the tables (WordPress does, that's why I'm asking).
Thanks for your help