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Boocock, 19, joined the BetVictor S/East club from Doncaster Rovers, and will continue his development with the club.
"The 19-year-old has impressed so far at the club and has now signed an extension until the middle of January," the club announced.
"This will be the first time Boocock has been involved in a busy festive period and it will be an excellent learning experience for him.
"Boocock plays alongside Rian McLean and Cody Prior who are also performing well at Sheffield."
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