Q:

Make static attribute immutable after declaration

Could I make static property final when it is defined in constructor, not on declaration?  
I know how can I create my custom class that creates immutable instances.  
But is it possible to make immutable object of some standard class? 
For example Object, JPanel, Calendar or anything else?  

A:

But is it possible to make immutable object of some standard class? 

No.  There's nothing in Java to support this.  All you can do is limit how widely published the reference is, and make sure that any code which has access to it doesn't mutate it.  You could create your own wrapper type which only exposes read-only operations, and expose that freely, of course. 
EDIT: As noted in comments, there's some support for this within the JDK, for collections - and Guava provides more thoroughly immutable collections and builders for them.  However, there's nothing general-purpose to take an object of any mutable type and give you back an immutable view of it.