our @ISA = 'Exporter'; is missing in the module. I forgot about that in my initial post. 
package Fleece;

use strict;
use warnings;

use Exporter;

our @ISA = 'Exporter';
our @EXPORT_OK = qw( $fleece );

our $fleece = "white as snow.\n";

1;

[download]

Tested.

In reply to Re^3: problem referencing global variable in self-written module by ikegami
in thread problem referencing global variable in self-written module by yburge

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