How to pass an activity context in an application to a service in an other application

Every Service has its own Context, just use that. You don't need to pass a Service an Activity's Context.

I don't see why you need a specific Activity's Context to call getSystemService() and a Service will receive Intents from a BroadcastReceiver as readily as any Activity.

Also, if the originating Activity is destroyed while this Service is running, the Context will be invalid or the Activity will be leaked.