EXPERT RESPONSE
Assuming that the server on this "mini-network" in your accounting office isn't connected to a domain, and it has user accounts configured for your accounting employees, simply moving the server from one room to another and connecting it to a different network won't change its access restrictions.
Anyone connecting to the machine -- again, assuming there are accounts configured on the machine and it wasn't secured solely by the fact it was in its own network -- will be prompted for credentials.
If not, just add some user accounts for only the people who need to access the server and remove anonymous access. You don't mention which operating system this server is running on or what services this server has provisioned (is it only a file server? Or is there server software for a particular accounting program?), so I can't give specific advice, but this general suggestion should pave the way.
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