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You can also charge a coil in series and discharge in parallel:

If You have two equal coils on the same core,
for simplicity each with 1 H and 1 Ohm,
connect them in series and You have 4 H and 2 Ohm,
put 1 V on them and wait until they are saturated:

1 V and 2 Ohm gives 0.5 A (A=V/Ohm)
4 H and 0.5 A gives 0.5 J (J=1/2 *H*I^2)
0.5 A and 4 H gives 2 Wb (A*H=Wb)

Then disconnect the source and at the same time connect the coils in parallel.
When in parallel You have 1 H and 0.5 Ohm.

If the magnetic flux is constant during the moment of disconnect and reconfiguration:

2 Wb and 1 H gives 2 A (A=Wb/H)
1 H and 2 A gives 2 J (J=1/2 *H*I^2)

Then we have an increase in energy by 400%.
Is this possible? (no)
Where is the error? (I forgot the N in ΦN=LI)
Maybe it will work using Edward Leedskalnin "Perpetual Motion Holder".

Try it in www.falstad.com simulator