All the coils are almost equal as wire length and inductance.
Input voltage is 12V. According to the theory, a voltage should be induced in L3 whenever there is current flowing through L1.
The current through L3 is blue, the current through L2 is yellow and the FG voltage is magenta. Let's see what happens:
Notice that the current through L3 flows during the time the MOSFET is off.
What if I disconnect L2?
So, L2 must be off while current flows through L3. It's about timing, we need to let the current through L3 flow, we need to let it's magnetic field grow without the magnetic field of L2 opposing.
I need opinions because I really wish to take this further and obtain some practical results.