I see... from the Facebook link the encoder is of the vertical variety and is mounted on a small carrier PCB. There appears to be no other electronic components (i.e. no resistors or capacitors) on the PCB.
I think you can make practically any rotary encoder work for you as long as it has a compatible shaft diameter and adequate shaft length. The number of "pulses per revolution" (PPR) shouldn't matter too much -- the Bourns one (PEC11R-4220F-S0024) in the Facebook posting has 24 PPR whereas the original has 36.
Another aspect in choosing a replacement is is get one without an anti-rotation tab. The original one has such a tab:

but the Bourns doesn't have one. It's unlikely that you'll be able to line up the tab with the matching hole in the faceplate, so just get an encoder that doesn't have the tab or one that you can break off.
So my checklist for a replacement:
- rotary encoder with switch
- around 36 detents
- vertical style encoder
- compatible shaft diameter and shaft length
- D-style shaft
- no anti-rotation tab
From what I can tell there is no need to use a PCB. You can just solder female jumper wires directly to the pins of the encoder and plug them into the pin header on the main PCB. Or use male jumper wires to plug into the existing cable. This pic shows how you might solder a wire from the encoder which then plugs directly into the cable:
