Java Happens-Before and Thread Safety

Suppose I have a class which wraps a HashMap as follows:

public final class MyClass{

     private final Map<String, String> map;

     //Called by Thread1
     public MyClass( int size ){
         this.map = new HashMap<String, String>( size );
     }

     //Only ever called by Thread2
     public final String put( String key, String val ){
        return map.put( key, value );
     }

     //Only ever called by Thread2
     public final String get( String key ){
        return map.get( key );
     }

     //Only ever called by Thread2
     public final void printMap(  ){
       //Format and print the contents of the map
     }

}

This class is initialized via "Thread1". However, the put, get, printMap and other operations are only ever called by "Thread2".

Am I correct in understanding that this class is thread safe as:

1. Since the reference to the map is declared final, all other threads would see the initial state of the map (happens-before is established).

2. Since put/get/printMap/etc are only ever called by Thread2, there is no need for mutual-exclusion.

Thank you