Networked printer

We have a remote location that has two thin clients. They connect, via RDP, to our main office’s Terminal server. Currently, at the remote office, we have a Lexmark printer connect directly to one of the thin clients and when they log on it creates a session printer on the terminal server so they can print. They want to get a networked copier. I’m wondering if I can set up that networked copier, on their thin clients so it will print to the hostname of the networked copier. The are connect to a router(DHCP) -and DSL modem. Thanks