Complex sentence: Right after his graduation, in 1893 Binyon started working for the Department of Printed Books of the British Museum, and in 1895 he was employed by the the Museum's Department of Prints and Drawings, under Campbell Dodgson.
Split into simpler sentences: Right after his graduation, in 1893 Binyon started working for the Department of Printed Books of the British Museum. In that same year, Binyon was employed into the the Museum's Department of Prints and Drawings, under Campbell Dodgson.