Can I transfer my license plate from my old car to a new car I'll be purchasing?

Here’s the scoop: I’m buying my grandpa’s car. He lives in FL; I live in CA. After I get the car, I plan on selling my old car immediately. Once I do, can I remove my license plate from my old car and put it on my new car? What would I need to do with the DMV around this? Thanks for any ideas, experiences, or links you have for me.