Legal Question in Business Law in California

Well your most immediate problem is if your father was the RMO of the corporation on the corporation's CSLB license. If so, you need a new licensee IMMEDIATELY. Any customer can refuse to pay you, and can even claw back payments, for any work done while you don't have a licensed RMO or RME.

If that's not a problem, or once you get that cleared up, you move to part 2. Transferring ownership is simple, the owner surrenders their shares to the corporation with instructions to transfer them to you. The corporation then issues you new shares. The problem is doing that legally and in compliance with probate law, while avoiding taxes on the transfer to the extent possible. That's not something you can do on your own without GREAT risk of it coming back to bite you. You need to see a probate lawyer about it, one with experience with intergenerational family business transfers, and if your dad had a will or trust, you'll need to have them look at that too.