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Are there any details about its course towards the moon?

4 months seems like a long time but presumably due to an ultra efficient trajectory.

>Hakuto-R’s path to the moon is a circuitous one, designed to require less fuel so the spacecraft can fit more scientific payloads aboard. Rather than flying straight there, it will use the gravity of Earth and the sun to give it an extra push during its four-month voyage. The 2-metre-tall craft will weigh about 1000 kilograms when it launches, but most of that mass is propellant that will be burned on the way, and the lander will have a mass of only 340 kilograms by the time it touches down.
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>Once it arrives at the moon, it will spend about two weeks in orbit, with each circle around the moon taking it closer to the surface. Finally, if all goes well, it will land softly in an area called Atlas crater.

https://www.newscientist.com/article/2348517-japanese-firm-ispace-is-racing-to-put-first-private-lander-on-the-moon/

https://www.nasaspaceflight.com/2022/11/hakuto-r-m1/

This has a more detailed description of the flight. But yeah I’m assuming it’s gotta be super efficient because it’s using a falcon 9 and they’re re-entering the boosters which further reduces its max payload.

If you check the website and scroll down you can see the trajectory they intend to use. It appears to use a low energy orbit that goes way past the moon before falling back towards it.

As far as I know, this is more because of fuel requirements on a tiny lander. If you go to the moon in 3 days, Apollo/Orion style, it takes a lot of fuel to slow down and enter orbit. This long trajectory however is low energy and saves up on a lot of fuel. Too bad we have to wait so long, lol.