If you really want a 1:1 transfer you will also need to save the Icinga CA of the current master.
If you don’t do that you will need the reconnect the satellites via the icinga2 node wizard to your new master instance.
If you are using the Icinga Director you can also do an export of the configuration done there via the Baskets.
Tbh I find the scenario somewhat strange. The master isn’t under your control but you can access it and are able to make copies/backups of such sensible data?
No, you will need the whole config “tree” as well, meaning host and service templates, check commands, apply rules etc.
I somewhat doubt that the owners will provide you the CA and databases though, as that is quite sensitive configuration/information, not limited to “your” systems.
If you get the basic templates, check commands and host objects as well as service config/apply rules you should be able to re-create the configuration and start from there with the master setup and a clean DB.
Setting up the new master and connecting the satellites to the new master via the icinga2 node wizard will create the necessary zones config.