The AKG MPAVL adapts a mini XLR plug that's on the C555L to standard XLR, which is what the tri-capture provides along with phantom power (48V).
What the tri-capture provides: INPUT1 (Mic) jack (XLR type, balanced, phantom power DC 48 V, 10mA Max)
What the C555L manual wants (relevant portions): For 9 to 52 V universal phantom power. Plug the mini XLR connector on the microphone cable all the way into the miniXLR socket on the connecting cable of the MPA V L. Connect the MPA V L to a balanced XLR microphone input with phantom power and switch the phantom power on.
As a side note, they're really charging too much for it since C555L is already natively 9-52V, so all it seems to do is adapt one plug into another, probably without any extra circuitry. Usually these types of adapters for other mics step the voltage down from 48V to <9V, but this one appears to just be a dumb adapter for $ludicrous (yay pro audio ripoff). Of course, there's not much alternative other than making your own plug for the C555L which might not work for whatever odd reason, along with voiding the warranty. /rant
BTW, these types of mics work great with IEMs for obvious reasons.