All calls on Uberconference are automatically recorded. I even figured out how to embed the recordings on Talk preset to when the conversation started. 
Unfortunately, only a handful of folks with Uberconference admin access can get the recording link, but, once shared, anyone can use the link. I’ve been contemplating a way to script publishing of uberconference recording links for OpenMRS… but just haven’t had the time to get around to it.
Screen sharing isn’t recorded (not a feature of Uberconference). In rare cases when I’m prepared for a call and someone is demonstrating something I think others will want to see, I’ll use my own copy of ScreenFlow for Mac to record the screen share and upload it YouTube.
<offtopic rant>
Having seen several Hangouts on Air recorded & shared by Andela devs, which records attendees + audio + shared screens and can be watched up to 2x speed, it makes me wonder if we should switch from Uberconference to Hangouts on Air; however, I think the show stopper is the lack of support for an open dial-in by phone option. If G Suite for Nonprofits supported recording of Google Hangout Meet meetings, it would be a no-brainer to switch (since Meet includes a call-in number).
</offtopic rant>