theres two possibilities
the first one,since i see the pics showing the first pinout on the fan doesnt soldered,the 2nd pinout was the VCC (5V) and the 3rd was data/sync (temp,etc) and the 4th are the GND,the 3rd seems the Data/sync and that shows 1V+,but i think it do share the data/sync ground pinout with gnd pinout like the common laptop fan pinout
the second one,since theres one pinout left,there seems possibility of VCC,Data+,Data-,GND pinout.
but as long the motherboard gain temperature data from sync/data pinout from the fan itself,it should be fine,thats why you can turn the laptop into fanless by bypassing the data/sync (cut the fan main power cable) without the VCC for fan itself.
many laptops fan came with only 3 pinout,but as long they can share same ground between the data and vcc,3 or 4 pin seems like work like the same.
hope it helps...
have a nice day
edit : after i seen first pics,seems like u need to just swap it to abc/cba
just test it,as long the VCC and GND doesnt get inversed,thats should be fine,always use the multimeter to test the GND and VCC on both of pinout,anyway whats the problem of the fan tho?,doesnt it get spin or it do get unexpected-turnoff,or wrong fan temp and speed info?