The rule you want is NF 5-2-2 (emphasis mine):
"When a foul occurs during a scrimmage down and ... [other conditions which are met here] ... the ball belongs to A or K after enforcement unless it is a 2-16-2g (post-scrimmage kick) foul. The number of the next down is the same as that of the down during which the foul occurred unless penalty acceptance includes a first down or loss of down, or the enforcement or the advance results in a first down. ..."
Just as if it were 1st, 2nd, or 3rd down, the offense gets the results of the play, the penalty yardage, and the chance to replay the down.
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