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Franks, who can play at centre-half or right-back, moves to the Blue Square Bet Premier side and joins fellow Dons Max Porter and Lee Minshull at the Welsh club.
The 21-year-old missed the start of the campaign through injury and has made just three appearances for Wimbledon, while he also had a spell on loan with Hayes & Yeading in October.
Midfielder Reece Jones has extended his loan with Blue Square Bet South side Hampton and Richmond Borough until the end of the season.
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