Виталий Мосейко, проэмулировал у себя на тестовом битриксе и все нормально сработало:
[CODE]//title:attach record
use \Bitrix\Main\Application,
\Bitrix\Main\Web\Uri,
\Bitrix\Main\Web\HttpClient;
// опции по умолчанию:
$options = array(
"redirect" => true,
"redirectMax" => 5,
"waitResponse" => true,
"version" => HttpClient::HTTP_1_0,
"disableSslVerification" => true,
);
$httpClient = new HttpClient($options);
$httpClient->post('https://**/rest/1/5ej0bc6cc6h5y1ql/telephony.externalCall.attachRecord/', array(
"CALL_ID" => '*****',
"FILENAME" => 'out-2754425-101-20181008-145938-1538999978.51.mp3',
"FILE_CONTENT" => [
'out-2754425-101-20181008-145938-1538999978.51.mp3',
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]
));
var_dump($httpClient->getResult());
[/CODE]