Wondering how to contact a C-Level Officer at a BB

SO.. My dad owns a REALLY small business, and a top C-level officer from one of the big 4 has been a customer of his for a fairly long time (Won't name any names, but you'll have heard of him). I'm just starting applications for an industrial placement year to happen within my time as undergrad at a semi-target Uni. I've done copious amounts of research on investment banking, so feel comfortable on technicals, and last year got top 10% GPA against my peers studying Economics.

I am going to apply to the IBD division at this firm. For obvious reasons it would be very beneficial to get the backing of this C-Level officer to help get my application through the door and get to interviews where hopefully I can demonstrate my skills.

My dad was thinking of an informal letter to the C-officers address, which I think is a good idea. Aside from the obvious, what should I include in this letter? That's what I'm looking for advice for, because this isn't quite the normal networking process that I'm aware of.

I was thinking it would be best to be addressed from my dad, explaining briefly their relationship and then about me, before buttering up the firm slightly and then asking: "to be put in touch with someone who could help best position my (sons') application for an interview with the firm in xyz division for xyz" (Sort of thing).

IS THIS THE RIGHT THING TO DO? I appreciate your guys' insight, please add anything you think I should put in, or completely trash what I was planning on asking and tell me what to ask instead - to get an interview.