You can NOT @Override a final method (§8.4.3.3); this much is clear. enum types (§8.9) are treated very specially in Java, which is why the equals is final (also clone, hashCode, etc.) It's simply not possible to @Override the equals method of an enum, nor would you really want to in a more typical usage scenario.
HOWEVER, looking at the big picture, it looks like you are trying to follow the pattern recommended in Effective Java 2nd Edition, Item 34: Emulate extensible enums with interfaces (see the language guide for more information about enum):
You have defined this interface (now documented explicitly for expected equals behavior):
public interface Group implements Group {
    public Point[] getCoordinates();
    /*
     * Compares the specified object with this Group for equality. Returns true
     * if and only if the specified object is also a Group with exactly the same
     * coordinates
     */
    @Override public boolean equals(Object o);
}
It is perfectly acceptable for an interface to define how equals method for implementors should behave, of course. This is exactly the case with, e.g. List.equals. An empty LinkedList is equals to an empty ArrayList and vice versa, because that's what the interface mandates.
In your case, you've chosen to implement some Group as enum. Unfortunately you now can't implement equals as per the specification, since it's final and you can't @Override it. However, since the objective is to comply to the Group type, you can use decorator pattern by having a ForwardingGroup as follows:
public class ForwardingGroup implements Group {
   final Group delegate;
   public ForwardingGroup(Group delegate) { this.delegate = delegate; }
   @Override public Point[] getCoordinates() {
       return delegate.getCoordinates();
   }
   @Override public boolean equals(Object o) {
       return ....; // insert your equals logic here!
   }
}
Now, instead of using your enum constants directly as Group, you wrap them in an instance of a ForwardingGroup. Now this Group object will have the desired equals behavior, as specified by the interface.
That is, instead of:
// before: using enum directly, equals doesn't behave as expected
Group g = BasicGroup.A;
You now have something like:
// after: using decorated enum constants for proper equals behavior
Group g = new ForwardingGroup(BasicGroup.A);
Additional notes
The fact that enum BasicGroups implements Group, even though it does not itself follow the specification of Group.equals, should be very clearly documented. Users must be warned that constants must be e.g. wrapped inside a ForwardingGroup for proper equals behavior.
Note also that you can cache instances of ForwardingGroup, one for each enum constants. This will help reduce the number of objects created. As per Effective Java 2nd Edition, Item 1: Consider static factory methods instead of constructors, you may consider having ForwardingGroup define a static getInstance(Group g) method instead of a constructor, allowing it to return cached instances.
I'm assuming that Group is an immutable type (Effective Java 2nd Edition, Item 15: Minimize mutability), or else you probably shouldn't implement it with enum in the first place. Given that, consider Effective Java 2nd Edition, Item 25: Prefer lists to arrays. You may choose to have getCoordinates() return a List<Point> instead of Point[]. You can use Collections.unmodifiableList (another decorator!), which will make the returned List immutable. By contrast, since arrays are mutable, you'd be forced to perform defensive copying when returning a Point[].
See also