Chosen Solution
I want to ask you for a favour. I was disassembling this projector and unfortunatelly break off fan connector (3-pin) from the board. I was trying to solder the connector back but on the place is missing coating and It not hold. I soldered it to another place but the fan isn´t going and projector indicates high temperature (red diod). Do anyone have any idea how to fix it? Is possible to solder only wires of the fan to the board (without connector)? Thank you for your advices. Blue circle shows a coating and red circle shows original place of connector
My idea to solve it which failed.
It’s hard to say just based on the pictures… Assuming the copper traces in (on or inside) the circuit board are still intact, I would opt to directly solder the wires to the pads at the bottom of the red circle. You could test those points with a multimeter to see if a voltage is present. You may need to scratch, very delicately, the solder mask (green layer) to expose some copper upon which you can solder. If you aren’t already using solder flux, I highly recommend it. If the traces are broken, you need to follow where the traces come from and then you could attach your fan there (you may need to lengthen your wires).