…Quick Fix…
 

If you are forwarding emails via rules or any other way for that matter and they are not getting to the external recipient the first thing you are likely to do is track the email to see if it’s leaving your Exchange servers. If you see the message:

Message Submitted to Categorizer

Then this may be the solution you are looking for

The the most likely solution is that Internet email forwarding isn’t switched on on your Exchange servers. To switch on simply do the following:

1.) Open up Exchange System Manger and expand Global Settings as below:

2.) Click Internet Message Format and then on the right hand frame right click and select properties and then click on the advanced tab as below.

3.) As you have probably guessed by now,click on the Allow automatic forward which will hopefully solve your problem.