In 2007, Mayer Brown LLP Partner Britt M. Miller met a 15-year-old girl from the South Side.Miller had signed up to volunteer as a mentor with LINK Unlimited Scholars. She sponsored that girl, Taylor Pickett, through her high school years and spent time mentoring her about once a month.Now, that former LINK student is a colleague.Pickett started as an attorney recruitment coordinator last month in Mayer Brown’s Chicago office.“Everything she has accomplished — she has accomplished it. I claim no credit …