I do not think that in fact it is possible to send a response to a private message through the api chart. I can understand why this may seem confusing, especially since it has a “commentary” relationship. From what I can collect from docs https://developers.facebook.com/docs/reference/login/extended-permissions/ permission "publish_actions" "Allows your application to publish content, comments and suggestions to the user thread" note that he only speaks the message to STREAM users.
I believe that Facebook did not approve of this ability because applications could potentially spam users. All they need is 1 legitimate message, and they can constantly respond with comments. Also, the https://developers.facebook.com/docs/reference/api/message/ message pages specifically list read only as an option.
You can also see the answer in this post.
how to send facebook message to friend via api chart using Accessstoken
Interestingly, the page account can respond to private messages if the user initiated it first. And the page can send only 2 responses without a response from the user. I guess this allows you to use 1 “answering machine” and then the actual response from someone contacting the user https://developers.facebook.com/docs/reference/api/page/#messages This will probably allow businesses to respond to customer requests.
I assume that any application cannot just send private messages, as the potential for spam will be huge if you have access to access_token. Obviously, there is a sending dialogue that addresses this, but I appreciate in your case that you want to reply to the message and not create a new one.
The Submit button says that it should be used in cases where the conversation is confidential, for example, if you can send an email.
https://developers.facebook.com/docs/reference/dialogs/send/
In the application situation, real means that you are requesting read_mailbox permission, then you can notify the user of your application that he has an unread message from a specific user. Then you can create a send dialog and fill in the To field using the uid of the friend who originally sent the message. This will then be displayed as part of the "comments" connection in the api explorer (I tested this)
The only caveat is that the user can, of course, add additional names in the send dialog and thereby start a new convoy.
hope this helps