That's a very early Witt ignition system. Those old blue box ignitions had a few issues. I had one on my Jota many years ago, but it died about 10 years ago and I replaced it with an Ignitech. You might be lucky and it'll work OK. It's worth a try anyway.
When converting from the old Bosch HKZ system, you need to replace those two small alternator coils (that you've already removed) with another charging coil like the one on the other side. You won't have enough alternator output with just the one alternator coil, because the Witt ignition system will be running off the bike's 12V electrical system (the HKZ system was independently powered by the coils you just removed). The alternator coils are readily available new from Laverda parts suppliers. Or you can get perfectly good used ones from anyone who has upgraded to a different type of alternator. I think I have a couple lying around, but I'm on the other side of the world.
You can run the bike without the additional charging coil for the purpose of road-testing the Moto Witt ignition. In fact, you don't need the alternator at all (as Maurice mentioned above). It'll run perfectly OK (for a while) if the battery is charged up.
The Witt ignition also used a different (two lobe) ignition rotor, which may be the one that's already fitted to the crankshaft. The rotor and extra charging coil usually come with the ignition kit, so if the previous owner gave you a heap of parts with the bike, the coil may be amongst them.
You'll also need a pair of ignition coils. One single output and one double. Any 3-5 Ohm coils from a Japanese bike should be OK.
There are a couple of ways to wire the alternator coils depending on the type of regulator/rectifier used (whether it's single or 3 phase). Note that you can't just retain the original unregulated rectifier when you add the extra charging coil. You'll need a voltage regulator. Most people buy a used one from a Japanese bike.
The Witt ignition is designed to use the Laverda's original VR pickups, so you'll need to re-attach some wires to those cut-off wire tails.
It looks like the previous owner intended to fit the Witt blue box in a Tupperware container. That's not a good idea because it needs cooling air.
There's plenty of info on installing the various Moto Witt ignitions on this forum if you use the search function.
There's also info in the library. Go to the Library section in the pull-down menus above. Select "Other manufacturer info", then "Moto Witt (DMC ignition)". Your blue box is a DMC1. There doesn't appear to be an installation instruction manual for the DMC1, but it's basically the same as for the DMC2. The differences are minor: As far as I recall, the DMC2 has a multi-pin connector and a different type of switch for selecting the advance curve.
