As soon as you get to Colorado, you'd report to a local unemployment office there, probably a phone system, and request that your claim be transferred. In fact, if you call your CA office, they will tell you exactly how to do this. You'll need a good address in CO, someplace for your checks to be mailed to, and a place there where you can do your job searches, a local employment/career center to base your registration for work.
But all the federal extensions are set to expire very soon anyhow. It won't really be relevant if they do. In the meantime, you'll take with you what goes with the extension you are on from your state, which is CA.
But a year from the date when your claim was originally filed, which is probably not going to be too long from now, you will have to be filing another claim. This will be a CA claim, to set up a new benefits year, regardless of what state you are living in, because that is where your wages are. At this point, you will not be able to draw from the new claim unless you have re-earnings, which means you have worked somewhere for a covered employer and have made enough wages to re-start benefits.
Either way, your drawing is coming to an end soon, unless they vote in a large new extension package. You'll have to ask in the individual state about how long and what you'll get. As I said, calling CA unemployment right now with your questions is a great place to start.