Java concurrency: is final field (initialized in constructor) thread-safe?

Yes it is. There is no way to modify the reference aMap itself, or add to the map after the constructor (barring reflection).

If you expose aMap it will not be, because two threads could then modify the map at the same time.

You could improve your class by making aMap unmodifiable via Collections.unmodifiableCollection or Collections.unmodifiableMap.

As already pointed out it's absolutely thread-safe, and final is important here due to its memory visibility effects.

Presence of final guarantees that other threads would see values in the map after constructor finished without any external synchronization. Without final it cannot be guaranteed in all cases, and you would need to use safe publication idioms when making newly constructed object available to other threads, namely (from Java Concurrency in Practice):

• Initializing an object reference from a static initializer;
• Storing a reference to it into a volatile field or AtomicReference;
• Storing a reference to it into a final field of a properly constructed object; or
• Storing a reference to it into a field that is properly guarded by a lock.