You can use a REST activity and export your data using an export mapping.
Here is documentation on mapping documents (which it seems you are already familiar with): https://docs.mendix.com/refguide/mapping-documents
Here is documentation on Consuming a REST API (which it seems you are also familiar with): https://docs.mendix.com/refguide/consumed-rest-services
To send data, you will choose the POST method in your REST microflow activity. Then in the Request tab of that activity, you’ll be able to specify an export mapping and pass an entity that will be sent in the body of the request.
Hope that helps,