Untested code below, but I think it should do the trick...

# First build a hash we can use to look up lines (keyed on 2nd line)
my %pairs;
open A, "<A";
while(<A>) { $pairs{<A>}=$_ }
close A;

# We use a third file
open C, ">C";
open B, "<B";
while(<B>) {
  # If this line matches a known 2nd line, insert it's 1st
  print C $pairs{$_} if exists $pairs{$_};
  # Always print the original line
  print C $_;
}
close B;
close C;
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