(in Source and Destination):

  our $storage; # or:
  # our Storage $storage; # I think this works to type it
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and in your main code:

  use Storage;
  my $storage = new Storage();
  use Source;
  use Destination;

  $Source::storage = $storage;
  $Destination::storage = $storage;
  my $input = 'source.txt';
  while (<IN>) {
    $source = new Source($_);
    $destination = new Destination();
    $source->storeData();
    $destination->useData();
  }
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in your Source and Destination classes, add code to handle setting a Storage object as a parameter to new().
then in your main code:

  use Storage;
  my $storage = new Storage();
  use Source;
  use Destination;
  my $input = 'source.txt';
  while (<IN>) {
     $source = new Source($_, storage => $storage);
     $destination = new Destination(storage => $storage);
     $source->storeData();
     $destination->useData();
  }
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