1. A screen transfer apparatus that communicates with a screen display apparatus that displays image data on a screen, comprising: an image data generation unit configured to generate image data to be displayed on the screen; an area identification unit configured to identify an overlapping area that overlaps with the image data for each of a plurality of divided areas into which the screen is divided, respectively; a division unit configured to divide respective partial image data belonging to respective overlapping areas in a vertical direction or a horizontal direction of the screen to generate divided image data for the respective divided areas, respectively; a data compression processor configured to compress respective divided image data belonging to the respective divided areas by using dictionary data obtained based on a predetermined amount of divided image data compressed in the past belonging to the respective divided areas so that compressed image data are generated for the respective divided areas; and a data transmission unit configured to transmit respective compressed image data belonging to the respective divided areas in an order defined according to a rule given in advance.