Assuming the only option is to record that Facebook Live stream, I think the only choice actually under your control would be to use a screen recorder program, like Bandicam mentioned already. It would appear that Facebook encrypts its live streams, so you can't rip the raw data stream.

Anything else would require using something other than Facebook live. For example, I believe Zoom allows participants to easily record what's being streamed right from the software (assuming the host hasn't forbidden it).