How to send Private Message using privatemsg_services module?
Here you go

To send new  message 

Endpoint: http://example.com/services/privatemsg

Content to Send (JSON Format) :

{
   "recipients": "xxx",
   "subject":"xxx",
   "body":"xxxx"
}


To reply a message for particular chat thread

Endpoint: http://example.com/services/privatemsg

{
"thread_id": "xxx",
"subject": "xxx",
"recipients":"xxx",
"body":"xxx"
}