To be honest, I don't think they'll pay a great deal of attention to what you put in your letter of application (providing you don't make a complete mess of it!).
With internal appointments the fact that you apply is sufficient, you will be judged on your record in your present post, and to some extent on your interview.
It may sound cynical, but I'd bet that as soon the present incumbent put their notice in the Personnel Manager asked the 'Big Cheese', "What are we going to do, give so-and-so the job; or get someone from outside?". Then if the outsider takes the boss's fancy, you've had it - if not - you'll get it!