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I met a hiring partner from a firm that is not attending my OCI at a networking event last week, and he told me I should send him an e-mail with my transcript and resume. I am going to assume he also wants a cover letter but am having trouble writing it. I am sure some TLSers have been in a similar spot.

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Well, maybe you can. If you were essentially invited to apply, I don't know that you need to write a formal cover letter. I'd write a personalized e-mail to the hiring partner touching upon why you're interested in the firm (hopefully you can frame it in terms of something you talked about at the networking event) and skip an attached cover letter.