With an eye on avoiding globals, with Two-arg open() considered dangerous in mind, and avoiding to slurping the entire input file or breaking it into lines when you're not going to need it split up that way anyway:

my $infile = "A.txt";
my $outfile = "B.txt";

open my $in_fh, '<', $infile
    or die "Couldn't open $infile for reading: $!\n";

open my $out_fh, '>>', $outfile
    or die "Couldn't open $outfile for appending: $!\n";

{
    local $/ = \65536; # read 64kb chunks
    while ( my $chunk = <$in_fh> ) { print $out_fh $chunk; }
}
[download]