I had this issue today with a scanner, a Samsung SCX 4623F.
If two computers are sharing the same printer/scanner, only the printer function will work on the PC that is using the printer by LAN (is not wired).
I’ve managed to fix the issue by installing a free software called “Blindscanner”. You can download the free version from here. The standard version is the free one. If this sounds too complicated, it is actually not. Installing this software is as easy as installing the drivers.
Download and install this software as it follows: on the PC that has the printer/scanner wired, install the server option. On the other PC that is using the printer/scanner by LAN, install the client option.
The server program should run all the time if you want to share the printer/scanner (it will auto-start when Windows is starting).
I had no issues by using this software on Windows XP.
If you want to scan more papers without having to click “next” all the time, select an option that is called “feed” or something, from the client program.
If you want to scan from the PC that has the printer/scanner wired, use the Samsung Scan and Fax utility program.