Is there an option to download/create a licence file? There should be an option to save the Standalone licence file. You can then add that licence file for the laptop version.
I've just done this today. The Office PC runs Altium, but I have a need to take a design away to a site and potentially tweak it whilst out and about. I have the project in Git (my own Git server), so I pushed the development branch up. Installed Altium on the laptop* and cloned the project down to it. I can make changes and push them back up to Git, then pull them down again on the PC when back. I have a standalone permanent licence, which is On-Demand, so I can move it between machines.
* The laptop is an Apple Silicon M1 Max MacBook Pro. I have the Arm version of Windows 11 installed via VMware Fusion, and Altium has gone into that. The Arm Windows has an x86 -> Arm emulator, so you can install Intel apps OK. Have to say, it's usable, which was a pleasant surprise. Previously I've just used remote desktop onto the Office PC via a VPN, but I thought I'd try this route.