Решение:
Получаем номер сессии GET запросом:
https://192.168.1.1:1500/ispmgr?authinfo=login:pass&out=json&func=auth&lang=ru
Отправляем POST запрос:
https://192.168.1.1:1500/ispmgr?auth=Номер_сессии&out=json
header:Content-type: application/x-www-form-urlencoded
Cookie: ispmgrses5=Номер_сессии;
ISP-Client: Web-interface
Referer: https://192.168.1.1:1500/ispmgr
content:[sok] => ok
[func] => file.edit
[elid] => file.php
[plid] => www
[full_filepath] => www/file.php
[encoding] => UTF-8
[fdata] => FILE CONTENT
Файл отредактирован.