Armstrong's new deal will keep him at the club until the 31st of December.
The full-back, 19, began his career with Burnley’s youth setup and came through the ranks there before joining Neil Reynolds’ side on loan for the start of this season.
He has made nine appearances so far this term, with FC United sitting top of the table with 27 points from 16 games.
The youngster will look to continue gaining first team experience before he heads back to the Clarets in the new year.
Photo credit FC United of Manchester
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