I did a remix for 4022 from same model. A community member asked me if I could do one for 6025 Fan, so here it is.
I don't have a 6025 so I can't test the fit but should work. I did print one and seems it will work.
Use the connectors that come with NOCTUA to connect the old fan adapter to the new fan as below (listed in order as in stock fab cable):
STOCK === NOCTUA
black → YELLOW
DarkGrey → BLACK
grey → GREEN
white → BLUE
4/15 EDIT:
Per user feedback I removed top right screw to allow wires clearance. First version works if you remove the clip holding the wires on the sidewall of the printer.
The author remixed this model.