Get converstion ID from message ID

When I create an admin initiated message from API https://developers.intercom.com/intercom-api-reference/reference#admin-initiated-conversation

I get no conversation_id in response.

Then, I cannot find this conversation or refer to it somehow. Although in contact's profile this message belongs to conversation with an id!

So, what I'm trying to achieve is to send a message to contact through API and then be able to save a link to this message.