I do not believe that is possible.
Since its the same printer, you might be able to trick the system and make it work, but generally, its not possible.
The first thing to do, is to remove the network share on the local computer so people cannot print to a printer that no longer exists.
Once a document is spooled to a printer, it is converted into a format that, that particular printer understands. Two different printers are likely to expect different formats. Simply moving a spooled document from one printer to another would cause the document to come out as garbage.
However, since you are actually using the same printer, you *might* be able to get away with moving the spooled document.
Find the location on your local computer, i.e., the computer that the printer was physically attached to, where spooled files are stored. Copy the spooled file to the location on the network where spooled files are stored. If your printer is a network ready printer, and it has its own built-in print server, you probably won't be able to do this. But if your printer is still a parallel lead, but hanging off another computer on the network, you may be able to accomplish this.
The default location for spooled files can be found in the registry at:
HKLM\Software\Microsoft\
Windows NT\CurrentVersion\Print\
Printers\DefaultSpoolDirectory
Once you have copied the spooled file, the printer *might* find the file and start attempting to print it, but it might not. If it doesn't, try restarting the print spooler.