Попробуйте это:
$crawler = $client->request('GET', 'https://www.petakids.com/spotlight/free-peta-kids-stickers/');
$form = $crawler->filter('#PETAKidsFreeStickers')->first()->form();
$crawler = $client->submit($form, array(
'strFName' => 'sayed',
'strLName' => 'sayed',
'strCompanyName' => 'sayed',
'strAddr1' => 'sayed',
'strCity' => 'sayed',
'strState' => 'AE',
'strEmail' => 'reovilsayed@gmail.com',
'strCountry' => 'Albania',
'strStateOther' => 'NONE',
'strZip' => '8440732',
'strPhone' => 1926184022,
));
Привет