Filtering in list view based on a related module's parameter

@manasan123
I decided that i would write solution fastest then wouldn’t speak about files and format.
custom/modules/Tasks/metadata/searchdefs.php

...
'advanced_search' => array(
...
    'contact_mobile' => array('name' => 'contact_mobile','label' => 'LBL_CONTACT_MOBILE','type' => 'varchar'),
...
),

custom/modules/Tasks/metadata/SearchFields.php

$searchFields['Tasks'] = array (
...
    'contact_mobile' => array(
        'query_type'=>'format',
        'operator' => 'subquery',
        'subquery' => "SELECT t.id FROM tasks AS t LEFT JOIN (contacts AS c) ON (c.id=t.contact_id) WHERE c.deleted='0' AND c.phone_mobile LIKE '%{0}%'",
        'db_field'=>array('id')
    ),
...
);

And you shoud add about label ‘LBL_CONTACT_MOBILE’ to your language file.