use strict;
use warnings;

my $file_in1 = '...';
my $file_in2 = '...';
my $file_out = '...';

open(my $fh_in1, '<', $file_in1)
   or die("Unable to open input file $file_in1: $!\n");

open(my $fh_in2, '<', $file_in2)
   or die("Unable to open input file $file_in2: $!\n");

open(my $fh_out, '>', $file_out)
   or die("Unable to create output file $file_out: $!\n");

my %cat2s_by_cat1;
while (<$fh_in2>) {
   chomp;
   my ($cat1, $cat2) = split /=/;
   push @{ $cat2s_by_cat1{$cat1} }, $cat2;
}

while (<$fh_in1>) {
   chomp;
   my @fields = split /=/;
   my $cat1 = $fields[-1];

   exists( $cat2s_by_cat1{$cat1} )
      or die("Cat1 $cat1 not found in file2\n");

   for my $cat2 ( @{ $cat2s_by_cat1{$cat1} } ) {
      print $fh_out (join('=', @fields, $cat2), "\n");
   }
}
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The code works! You are amazing! Thank you so much!