Version 1.3.2 of the Desktop call recorder is now available, which includes an automated feature for recording Facebook Messenger calls. However, this feature is only compatible with the desktop version of Messenger. For the web version, the app still supports manual call recording.
During the beta testing phase, the "Desktop call recorder" app can be downloaded and used for free. After beta testing ends, it will remain free for personal use, subject to a fair usage policy.
You can download version 1.3.2 of the "Desktop call recorder" app at https://desktopcallrecorder.com/.