how to share a scope variable with ng-app's in AngularJS

You have to use angularjs service for this purpose.Hope the following implementation will help you to get some understanding

angular.module('app.A', [])
.service('ServiceA', function() {
    this.getValue = function() {
        return this.myValue;
    };

    this.setValue = function(newValue) {
        this.myValue = newValue;
    }
});

angular.module('app.B', ['app.A'])
.service('ServiceB', function(ServiceA) {
    this.getValue = function() {
        return ServiceA.getValue();
    };

    this.setValue = function() {
        ServiceA.setValue('New value');
    }
});

You can share data between Angular apps by Window postMessage and / or localStorage.

Just wrap postMessave into Angular Service and propagate changes on post event.