Your code looks strange for me because when I see get method it basically means that the bean has a such variable or at least pretending to have it. Why can't you just name your method "login" in your JSF bean?
If i use just a simple 'login', the application hangs with a "javax.el.MethodNotFoundException".
If i use <h:commandButton... instead <a4j:commandButton... i must use only simple 'login' and it works.
Does i use <a4j:commandButton... i must call 'getLogin', original mthod name, so that my
application works correct.
In case of a4j:commandButton or h:commandButton you should use the full name of method because it's an action method. JSF uses property-like access to methods only when it's supposed to be a field of a bean. In case of an action method it should be the full name. And I suggest you to name the method inside the bean login but not getLogin. It's not a good approach when your getters start holding any bussiness logic(Some times they can contain some converting/valiudation/checks but not a call of bussiness methods).
Now i understand the problem. In an action method i must deliver the original full method name.
That was my misunderstanding.