The Collaborative International Dictionary of English v.0.48:

Telegrapher \Te*leg"ra*pher\, n.
   One who sends telegraphic messages; a telegraphic operator; a
   telegraphist.
   [1913 Webster]

WordNet (r) 3.0 (2006):

telegrapher
    n 1: someone who transmits messages by telegraph [syn:
         telegrapher, telegraphist, telegraph operator]