In ALM Site Admin, you can click and drag a project from one domain to another (like from "Default" to some other named domain)

BUT

This does NOT change where the repository folder corresponding to the project in the folder structure on the drive (e.g. "c:ProgramDataMicro FocusALMRepositoryqcDefault", where "qc" is the parent for ALL domains, and "Default" is one of the domains).

So, if you just do simple drag/drop in site Admin, you would be done quickly, AND the project would "look and act" like it was in the new domain,  BUT if you wanted to later migrate or backup just one domain's project repositories, you would miss some as those projects would have their repositories in the "wrong" domain -- not as obvious as all stored under the SAME domain folder (you COULD still select project repository folders one by one under different domain folders if you want).

In this case, your request mentions that a "division" of the company wants their projects moved to a specific domain. This leads us to believe there might also need to be some segregation of the repositories for backup/migration purposes (e.g. point to ONE folder to backup or move with children folders, etc.)

I would recommend instead of drag/drop in Site Admin, to do more "formal" remove/restore process:

1. click on project to be moved
2. Take note of Project directory (path) shown on Project Details tab and navigate to this path in a file manager/file explorer
3. rt-click REMOVE project
4. Your dbid.xml file in the project directory will be updated as you do the "remove" and project will disappear from project tree in Site Admin (ALM not talking to it any more)
5. Create (or select existing) desired new Domain and select it in tree in Site Admin to see the "Physical directory" associated with it (ex. Domain "Billing" might be "c:ProgramDataMicro FocusALMRepositoryqcBilling_2")
6. Using file manager/explorer MOVE your project's folder to now be under the NEW domain folder (e.g move from being a "child" folder of "c:ProgramDataMicro FocusALMRepositoryqcDefault" to now being a child of "c:ProgramDataMicro FocusALMRepositoryqcBilling_2", where "Billing_2" is the name of the folder for the new domain).
7. Now click on new/desired domain, rt-click and select RESTORE Project, choose dbid.xml file from moved project repository folder location in newly copied folder structure.
8. When completed, the project will show back up in the new domain in the project tree in Site Admin.

This is most easily accomplished while running Site Admin on the ALM server as the dbid.xml files are all local.