Federal authorities are in the preliminary stages of investigating the handling of classified material found at former President Donald J. Trump’s Florida home after he left office, people familiar with the matter said on Thursday. The effort, led by the F.B.I., stems from the discovery of classified information in 15 boxes that contained documents, mementos, gifts and letters that had been taken from the White House at the end of Mr. Trump’s term in apparent violation of the requirements for turning over all presidential records to the National Archives. The development was reported earlier by The Washington Post.