There are a whole lot of ways to capture a feed from a presenters laptop. Here are three options that’ll give you a recording clean feed during your live production.
Direct feed over HDMI
Inserting a splitter between the presenter’s laptop and the projector is probably your best bet. It will ensure a high-quality image of whatever they are showing.
Running a long HDMI cable comes with its problems, so consider using a HDMI to SDI converter or HDMI network extender to get the job done at a long distance.
Wireless apps
If you are running something like Wirecast, you may find that there is already an app for that. In this instance, you could install Telestream Desktop Presenter onto the presenter’s laptop and use it to bring a feed into your Wirecast production.
The good part is that it’s available for MacOS and Windows, the bad part is that you will, of course, need to install it on their machine.
Record on the laptop
As a final option, you could just use something like Quicktime on the presenter’s laptop to record. This will mean getting in there and pressing start/stop and making sure you take the recording with you after the event.
I would only use this as a last resort, but it could be your only option!