Michelle Obama’s favorite threads shop has been sold. Preppy clothing retailer J. Crew completed a deal Tuesday with buyout firms TPG Capital, a former owner of the company, and Leonard Green & Partners to purchase the clothier for $3 billion, or $43.50 a share. The purchase price would be 16 percent higher than Monday’s closing price of $37.65 a share, after the company’s stock jumped 1.6 percent in anticipation of strong earnings. Millard S. Drexler, the storied executive who earned the nickname “Merchant Prince,” for his success with Gap in the 1990s, led J. Crew’s reinvention as a fashionable clothing retailer and will remain at the helm.