Jolla1 did have facility to record calls, I’m looking at the settings page for Phone right now, under the “Call recording” submenu. (Settings/Apps/Phone) (SFOS 3.4).
One option to turn call recording on/off and the other is ‘Recorded calls’, tap on this, another window opens showing recorded calls, if any. As for sharing, no idea, that may require some manual input to shift the recorded message to where it can be sent, it may also mean changing the file extension to something like ‘.txt’ to make it acceptable for sending by BT for example.