It's generically known as a "Laplink parallel cable". These also came in a 6-connector called something like a "Laplink Universal Cable", with both DE-9F and DB-25F for serial and DB-25M for parallel.
I still have a carton of new unopened-in-the-bag parallel cables, which can also be used with Microsoft Interlink. We had them custom made to our specs, as the consumer-level ones were, in our opinion, a bit flimsy.
...I remember using this in the early to mid 1990s with a tool by the name FX.com.
Might that be FastLynx? It's also sometimes known as "FX" (fx.exe) and should do exactly what you need. I use FastLynx v2.0 and a Belkin F3X171-10 ("Pro Series File Transfer - PC to PC Cable - Serial") to transfer stuff between PCs.
Indeed it is dead simple. One thing to remember is that interlnk.exe has to be loaded with your config.sys. intersvr.exe can be loaded from the command line at any time.You can use interlnk/intersvr.exe that were part of DOS 6-6.22. As I recall, you run intersvr.exe on one machine and interlnk.exe on the other. It's been a long time since I needed to do it, but it was very straightforward.
Indeed it is dead simple. One thing to remember is that interlnk.exe has to be loaded with your config.sys. intersvr.exe can be loaded from the command line at any time.
Also, if you put intersvr.exe in your autoexec.bat and you can have a headless box. I've had one of those as part of the network mix since 6.0 came out.
I will experiment with that as well. Now I need to buy one of those cables.
Let's not forget the IBM "Data Migration Facility", released at the time of the initial PS/2s (1987, DOS 3.3). Intended to primarily support moving data from 5-1/4" floppies to 3-1/2", you can do rudimentary copying to a harddrive as well. Documented here: http://ibmmuseum.com/ohlandl/floppy/Data_Migration_Facility.html
I am running MS-DOS 6.22 on my 425SI/SI and PC-DOS (I forget the version #) on my 325T so I would need to downgrade.
Yesterday when I looked the page I saw how Louis had written it too. Those are the minimum PC-DOS versions (2.0 or higher on the "sending" system, 3.3 or higher on the "receiving" system"). The "receiving" portion executable was even included on the Reference Diskettes of the PS/2s.
With some older systems, receiving files might be more hardware-dependent than the DOS version: The bi-directional printer port ("EPP" now, but initially know as a PS/2 parallel port) has to be present, and there isn't any mechanism to drop down to a "nibble" mode if not. All PS/2s had bi-directional parallel ports (a few third-party adapters specifically for them did not), and the microchannel level (Model 50 and above) had 16550-level UARTs (again, some adapters were 16450).