Pic 1 is the starter. I wired one of those as an apprentice.
Push the handle down, it puts the rotor and stator in series for start up, but won't lock in that position, you have to hold it.
Once the motor reaches full speed let go of the handle, then pull it up. That puts the windings in parallel run mode and the solenoid holds it there.
EM stop or power failure and the starter drops out of run mode back to it's central OFF position. (note that wouldn't meet current safety requirements, but that was how it was done then)
I also wired a 3 phase star delta version but that was switched with contactors.
But it was all a long time ago.
There are probably 2 stator windings, and the capacitor gives the phase shift to one of the windings to determine the motor's direction.
I would guess in that case that A1 and A2 is one stator winding, A2, A3 is the other stator, and Z1 Z2 is the rotor. Can you try some measurements with an ohm meter to see if that is true?
Can you find a model or part number on that starter, perhaps a google search might reveal the connections, otherwise it's going to take a lot of working out to determine what connects to what and probably beyond a forum looking at pictures.
The box above the starter, just out of the top of pic 1 will be the isolator. So you have the input supply connections to the starter identified.
So if you fancy trying some live tests (usual live working precautions) apply power to the input, put the starter to RUN mode, and determine where the supply comes out of. As both rotor and stator will be in parallel in run mode, you should find L and N each coming out from 2 places. One will be the rotor connections, and the other the stator connections. You can also of course determine that with dead tests with an ohm meter which is probably much safer.
Usual disclaimer, if you re not 100% confident, don't try that.
Once you have identified the two output pairs, connect it up and give it a try. One pair will go directly to the rotor, the other pair will go directly to one stator, and via the capacitors to the other stator.