Ok, so here is what I suggest you get two programs. The best program I have for you that is free is OBS Studio. (www.techradar.com/news/the-best-free-screen-recorder) if you want to choose a different click on that site. Also if your going to transfer the file to mac, I advise you use a usb. If that isn't what your talking about, in the output (after or before video records) you can change the file so mac can acess it. (.mov, .avi, etc...) If you need more info ask me.
For your Windows computer to your Macbook Air ? You can use software I think like:
But can you tell me the exact goal? Because I use the following tool to talk to my VA's (Virtual Assistants). I use a free tool called Loom.
This is a chrome plugin, and it captures my screen, I do my stuff I need to show, then I stop the recording and the recording is automatically uploaded on the internet. So you just sent the link to the one that wants to see the screen recording.
But if you want the real .mp4, .avi file on your macbook air and not on the internet, I would use camtasia, or the other alternatives I showed to record it. Look in Google for Camtasia free alternatives if you want something free like FRAPS.
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