Hi Ramses,
@imicrosoldering, AKA Chris is our resident expert on microsoldering, which is what is going to be required to fix your phone. I'll tell you what I know, but he's the authority on things like this.
First off, the circuit board on your phone actually consists of two boards sandwiched together, and to properly repair it my understanding is that the boards need to be separated first, which requires specialized equipment and expertise. Once the boards are apart, a heat gun usually used to remove and replace the connector, and again, it takes an experienced technician to do it right and not cause further damage to the board.
The upshot is that unless you are experienced in microsoldering and have the proper equipment, this is a repair best left to a professional. I consider myself fairly experienced at soldering, but this isn't a repair I would attempt.
You will want to find a repair shop qualified to replace the OLED FPC connector to do the job. They should be able to give you a reasonable idea of cost before they start and should stand behind their repair in the case of any incidental damage they cause in the course of the repair.
Hopefully Chris will hop in here to correct anything I've gotten wrong and add any further information you need to know.