The less formal word tell is sometimes more suitable than inform, especially in letters that we want to make friendly.
"Please tell me", or "Please let me know ", is less stiff than "Kindly inform me".
Inform cannot be used with a verb in the infinitive, and the writer of this sentence has gone wrong:
I am informing the branch to grant this application.
He should have said telling or asking.
Moreover, inform seems to attract adverbs as prim as itself, sometimes almost menacing. In kindly inform me the politeness rings hollow; all it does is to put a frigid and magisterial tone into your request. Perhaps you will inform me means, in officialese, that you have got to inform me, and no "perhaps" about it, and I suspect the consequences may be serious for you.