Well seems it is a quite old post, but well no answers, so I hope it helps someone. You could have used example from the following repository Telegram Bot Client in PHP that I am currently developing. This is the method I used to send message.
// initialise variables here
$chat_id = 1231231231;
// path to the picture,
$text = 'your text goes here';
// following ones are optional, so could be set as null
$disable_web_page_preview = null;
$reply_to_message_id = null;
$reply_markup = null;
$data = array(
'chat_id' => urlencode($chat_id),
'text' => urlencode($text),
'disable_web_page_preview' => urlencode($disable_web_page_preview),
'reply_to_message_id' => urlencode($reply_to_message_id),
'reply_markup' => urlencode($reply_markup)
);
$url = https://api.telegram.org/botYOUR_TOKEN_GOES_HERE/sendMessage;
// open connection
$ch = curl_init();
// set the url
curl_setopt($ch, CURLOPT_URL, $url);
// number of POST vars
curl_setopt($ch, CURLOPT_POST, count($data));
// POST data
curl_setopt($ch, CURLOPT_POSTFIELDS, $data);
// To display result of curl
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
// execute post
$result = curl_exec($ch);
// close connection
curl_close($ch);