Is it possible to convert voice mail into text using PHP? Is there any 3rd party voice to text converting software works well with PHP?
Not PHP, but you could use this as a open-source backend and make the necessary calls from PHP to system (exec, system etc.): http://cmusphinx.sourceforge.net/
You can also check this tutorial (although commercial probably): https://www.twilio.com/docs/tutorials/walkthrough/ivr-screening/php/laravel
Where the voicemail to text function relies on the Transcription Resource of the API. https://www.twilio.com/docs/api/rest/transcription