Reg: H1B transfer after I-140 approval

Hello friends,
My I-140 EB2 is approved recently through my consulting company. I am in 6th year of my H1. I would like to move to a full time employment with a reputed company.

I know we can port port our priority date. But would like to know, once I transfer transfer my H1B to another employer (assuming I get 1-3 yrs of validity),

i) How soon the new employer should file my Labor? (As we know, most good organizations take 6 -12 months to even start the process.) Or should it be started right away at the time of joining?

ii) When is the best time to make a switch? I mean after getting extension from my current employer or it doesn’t matter?