If you have control of the source of Class1, not just Class2, you can
use serialization on a private object. Note: myMth2 accepts (recursive)
calls from any methods that it calls.

package pkg1;
import pkg2.Cls2;
public final class Cls1 {
  private Object srlzr=new Object();
  void myMth1(Cls2 whom) {
    ...
    synchronized(srlzr) {
      // Only pkg1.Cls1.myMth1 synchronizes on srlzr.
      whom.myMth2(this, ...);
    }
    ...
  }
  public void isItReallyYou() {
    // Throws Exception if not synchronized on srlzr.
    // If caller synchronized on srlzr, does nothing.
    srlzr.notify();
  }
}
--------------------
package pkg2;
import pkg1.Cls1;
public class Cls2 {
  public void myMth2(Cls1 which, ...) {
    // isItReallyYou throws an Exception unless myMth2
    // was called from pkg1.Cls1.myMth1.
    try {
      which.isItReallyYou();
    } catch (IllegalMonitorStateException m) {
      throw SecurityException();
    }
    ...
  }
}

--Mike Amling