So if so, when does it happen? Let's I assume I pass the theory, CPL, IR, ME & MCC. I have 250h (or just under) of flight time. I have done the modules at different schools.
I'm not an official fATPL, right? Can someone please explain to me what is meant to happen next?
Once you've been flying MPA for a while, and are close to achieving the required experience, you can ask your examiner as a part of the normal LPC/OPC cycle to conduct the additional items required to complete the ATPL skill test. As MJ has said, it amounts to a few extra items including a raw data ILS.
http://www.caa.co.uk/docs/33/SRG2199FFenabled.pdf
http://www.caa.co.uk/docs/33/SRG1158WEB.pdf