Sony Xperia Z5 comes with built-in answering machine (read more at http://ccm.net/faq/43015-sony-xperia-z-how-to-enable-the-answering-machine)
What it does it after x number of seconds, Xperia Z5 will run the greeting and save the recording on the phone. Not through the cell phone provider.
When I turn on Xperia Z5 and ACR, after my greeting, ACR steps in and disconnect the phone. People can not leave messages for me at all.
If I turn off ACR, then the Z5 answering machine works well.