You are perpetually authorized to initialize a final variable. The compiler makes it certain that you can perform it only once.
Perceive that calling methods on an object saved in a final variable has nothing to act with the semantics of the final. In other words: the final is simply about the citation itself, and not about the contents of the referenced object.
Java has no notion of object immutability; this is accomplished by deliberately creating the object, and is a far-from-trivial effort.