Yes.
You should get FP done before changing your job. That's my experience, cause my friend did the same thing, but didn't finish FP. The case had been transfered to new local SC.
If you don't have to change your job, just be patient and wait to get it approved. The speed of processing is fast now. Nobody can say it's no any problems. Actually, we didn't know so many details before changing the job and we were worried about it so much untill we got it approved.
Good luck!