LOSS OF SEPARATION OCCURRED WHEN A ZDC ARTCC RADAR TRAINEE CTLR HANDED OFF A B767 TO THE WRONG SECTOR.

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I WAS PROVIDING OJT AND DID NOT NOTICE THAT MY TRAINEE HANDED OFF AN ACFT TO THE WRONG SECTOR. SHE APPARENTLY THOUGHT SHE HAD HANDED OFF TO THE CORRECT SECTOR AS EVIDENCED BY HER COMS XFER TO THE PROPER SECTOR. UNFORTUNATELY; THE SECTOR THAT RECEIVED THE COMMON CHANGE DID NOT ASCERTAIN THAT THE ACFT BELONGED TO HIM. ALSO UNFORTUNATE WAS THE FACT THAT THE SECTOR THAT ACCEPTED THE HDOF WAS NEXT TO RECEIVE THE ACFT; ALTHOUGH NOT FOR ANOTHER 130 MI. I HAD 42 SECONDS TO NOTICE THE ACFT IN HDOF STATUS TO THE INCORRECT SECTOR AND WAS BUSY WITH OTHER TFC SITS IN THE SECTOR. ONCE THAT OPPORTUNITY WAS GONE; THERE WERE SEVERAL WAYS THE ERROR STILL COULD HAVE BEEN PREVENTED: 1) THE SECTOR RECEIVING THE COM XFER COULD HAVE REQUESTED A DATA BLOCK; RATHER THAN; OR IN ADDITION TO; ASKING THE COMPUTER WHICH SECTOR HAD TRACK CTL. 2) THAT SAME SECTOR; STAFFED BY R&D POS; COULD HAVE NOTICED THE INTRUDER'S TARGET. 3) THE SECTOR THAT ACCEPTED THE HDOF 130 MI EARLY COULD HAVE THOUGHT IT UNUSUAL TO BE RECEIVING SUCH AN EARLY HDOF AND 'QUICK-LOOKED' THE PREVIOUS SECTOR. 4) THE SAME SECTOR; IF ACCEPTING AN EARLY HDOF; SHOULD HAVE PROVIDED TA'S; AND COULD POSSIBLY HAVE SEEN THE TFC.