The US Postal Service began home delivery in Sugar Land in July 1956, which is the date of this photo. The Post Office was then located in the shopping center; it looks to me as if they are standing at the rear entrance to the shopping center.
Left to right: Mrs. Nena Mae Iiams, Post Mistress, Meinert Pundt, Mail Carrier, John Hess, Mail Carrier, Mrs. Carroll Smith Rome, Parcel Post Carrier, and W. R. Warrick, Postal Inspector.