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; }
}