No, it doesn't help. It still sorts correctly: 
#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say fc };

*ARGV = *DATA{IO};

my $column_line = "";
$column_line = <> while $column_line !~ /Invoice ID/i;
chomp( my @columns = split /\t/, $column_line );

chomp( my @data_lines = <> );

# Sort the data lines according to the "Company Name" field, and then 
+the "Invoice ID" field.
my ($company_name_index) = grep { $columns[$_] eq "Company Name" } 0 .
+. $#columns;
my ($invoice_ID_index) = grep { $columns[$_] eq "Invoice ID" } 0 .. $#
+columns;
@data_lines = sort {
    my ($company_name_a, $invoice_ID_a) = (split /\t/, $a)[$company_na
+me_index, $invoice_ID_index];
    my ($company_name_b, $invoice_ID_b) = (split /\t/, $b)[$company_na
+me_index, $invoice_ID_index];
    fc($company_name_a) cmp fc($company_name_b) or
    $invoice_ID_a <=> $invoice_ID_b
} @data_lines;

print "Replacement Header Text Here\n\n$column_line";
say for @data_lines;

__DATA__
Original Header Text    
    
Invoice ID    Company Name
1    SEBASTIAN COMMUNICATIONS
2    MASQUE SOUND
3    SEALEVEL SYSTEMS
4    MASSTECH, INC
5    SE INTERNATIONAL
6    SOUTHEAST SERVO, LLC
7    SEALEVEL SYSTEMS, INC.
8    MASTERBILT

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My guess: the indices are wrong. Your code sorts the file by a different column. 
($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,

[download]

In reply to Re^3: Sorting an array of strings when some of the strings have commas in them? by choroba
in thread Sorting an array of strings when some of the strings have commas in them? by perldigious

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