There are a couple of problems here. my means lexical scoping, which means the my $HoH in hash isn't supposed to be accessible anywhere else. $HoH in hash is a hashref; then the main code expects a hash.

You'd be better off with use, but it's not necessary. Starting hash like this:

package hash;
%HoH = (
         'HASH_1' => {
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and using this for the main routine would work:

#!/usr/bin/perl -w
use strict;
use Data::Dumper;
require 'hash';
print Dumper($hash::HoH);
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or, you could have hash assign directly to the main namespace:

$main::HoH = {
         'HASH_1' => {
                item_a => "abc",
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and then

#!/usr/bin/perl -w
use strict;
use Data::Dumper;
require 'hash';
print Dumper($main::HoH);
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(These are examples of what is possible, not what's recommended.)