Join is a pretty cool app. It can do a variety of things, from sending texts to transferring files across your variety of different devices. Developer joaomgcd has added another feature to its extensive arsenal, making it easy to record an Android phone or tablet's screen from another device.
Screen Capture with optional upload to YouTube. Check link.
No longer requires Contacts permission. Only requests SMS permission when needed
Made "Reply Directly" action available for KitKat devices
Added Dutch and Russian translations
Clipboard bubble now remembers vertical position you last dragged it to
When notifications are requested, all notifications are sent
Other bug fixes
The way this works is pretty simple: on a device with Join on it (this can be another Android, the Windows 10 app, or the Chrome extension), tap on one of the Android devices to see the list of actions, and select 'Toggle Screen Capture.' This will then record the screen of said phone or tablet. Once you've finished capturing, tap 'Toggle Screen Capture' again to finish the recording.
The video can be optionally uploaded to YouTube, or pushed to your PC or other such device. Other new things in this release include the removal of the Contacts permission, and other improvements and fixes. The update is available on the Play Store now, or at APK Mirror.