BTT UPS module?  

RE: BTT UPS module?

What you describe is easily explained, I think.

The Prusa has "Power Panic" which basically monitors the line voltage coming into the printer.  If the voltage goes too low or completely stops, even for an instant, this triggers a sequence designed to save the print after a shutdown.  To do this, it uses the remaining power stored in the Power Supply's capacitors to do an orderly shutdown and remember where it was and what it was doing..  To be effective, it needs to react quickly as the power stored in the capacitors will run out quickly.  As it cannot determine if a power outage is going to be for half a second, a minute or  several hours, it shuts down and hopefully saves what it was doing for later recovery.

A printer without a quick-reacting Power Panic might run perfectly fine for a second or two without line voltage and continue the print without interruption using the power stored in the power supply's capacitors.  If the power runs out, the print is ruined.

The device you linked  to appears to be a capacitor bank that adds a lot of additional capacitance, many times greater that the Power Supply's internal capacitance, and signals the board for an orderly pause then shutdown.  To make it work on a Prusa would involve disabling the Power Panic and modifying the firmware.   If you have to ask how, my advice is not to do it.    Also, if such a device is not well designed, it could damage the Power Supply and multiple Farads of capacitance can present a considerable danger if a short circuit occurs.