A Salvador Dali painting stolen last week from a New York City gallery was mailed back in pristine condition, police said Friday. Hope had been raised earlier this week when the gallery received a brief email message by an unknown person, saying the 1949 ink and watercolor “Cartel de Don Juan Tenirio” is “on its way back to you already,” police said. It was mailed from Europe, and bore a phony sender name and address, Deputy New York Police Commissioner John McCarthy said. A spokesman for the gallery, which opened this year on Manhattan’s Upper East Side, declined to comment. A second police source speculated that publicity surrounding the theft had complicated efforts to sell the painting on the black market. Police detectives, including the department’s in-house art expert, Detective Mark K. Fishstein, received the painting from postal inspectors at John F. Kennedy International Airport when it arrived in New York Thursday. It was returned Friday to the gallery, where it is being authenticated, McCarthy said. Last week, a man visiting the gallery removed the painting from a gallery wall, placed it in a shopping bag, and walked out of the building. Fishstein, the Brooklyn-born son of two antiques dealers, became the department’s “art cop” in 2003 after he caught the attention of his superiors as a young patrol officer, McCarthy said. Fishstein had been called to woman who had been found dead. His sergeant had just finished an inventory of the apartment’s valuables when Fishstein suggested police secure the painting on the wall. “Why?” his sergeant asked. “It’s an original Picasso,” he replied. In 2008, he arrested a couple who had stolen a $100,000 Andy Warhol print of Chinese communist leader Mao Zedong from a frame store.