Re: e.g. Your ref AB/ pb in business letters
This is a rather old-fashioned practice, but yes, Alice Bennet may be the person who signed the letter, but Patricia Barker was the typist, and likewise, Marcia Newbury was the person who signed it, and Tom Henderson typed it.
(So few people dictate their letters to be typed that I haven't seen this in ages.)
I don't know what the "your ref" "our ref" means.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.