Option 1: Screen Recording Software
You start by broadcasting your live stream. When you’re ready to record your video for re-purposing, open the replay link (click here for how to).
The next step is to use a screen-recording program. There are several out there butCamStudio is a good place to start looking. Their software is free and produces high quality recordings.
Finally, You will play your Periscope video while running your recording software.
Once again you will start by simply broadcasting your live stream. Then, when you want to record your video you will run a mobile screen capturing app like Screenshot Ultimate for Android. Unfortunately Apple does not allow screen capturing apps to run through your phone. There are a few however that run through your computer, but they usually cost to download.