With this idea, the advantages of moving the ISS (or parts of the ISS) to Moon's South Pole are the following :
International agreements do not have to be rewritten.
The cost of the operation is beneficial because :
A new complex do not have to be built (meaning new materials do not have to be moved into Earth's orbit then to the Moon).
Moving the ISS from LEO (Low Earth Orbit) to Moon's ground is cheaper than progressively moving parts and segments from Earth's ground to Earth's orbit and then to the Moon.
Sending the same anthropological mass as the ISS (~ 450 Tons) on Moon's ground would inevitably be more expensive.
ISS solar panels are already set up and functional.
ISS onboard water and air cycling systems are already set up and functional.
ISS muscular-atrophy countering equipment is already set up and functional (and built for a lower gravitational environment, meaning it is more than practical on the Moon).
There's no living environment adaptation time required for the Astronauts (they already know the ISS).
Once the operation started, the inside of the ISS could be filled with materials and tools for further human landing (water, drones, etc.).
To ensure cosmic rays bombardment isolation, micro-meteoroids protection, thermal isolation, several layers of lunar regolith can be put above ISS' sensible parts (like it was proposed for some Moon bases design, see here).
To limit the psycho-socials effects of a ISS loss for Humankind (if it would have to be deorbited into the Ocean as stated), for such a complex structure is a pillar of our modern civilization, our success, our States and Agencies agreements, but also a driver of cultural content (art, films, series, music) or vocations (engineering, science, astrophysics, Astronauts, etc.), as well as maintaining a positive image of going to space or studying it (from children to scientists). If it is reduced into ashes, a huge part of Humankind's heritage would be lost.
After several years of use as a Moon ground station, remains of the ISS could also be used or monetized as :
A Moon tourism destination, like a Museum.
A stock of specials part for further Moon builds or maintenance (like mechanical parts, wiring, etc.).
And finally, to take an advantage in the new space race in a Occidental (and partners) coordinated effort to move faster, at cheaper cost, than competitors. In this context, naming : CNSA and Rocosmos.
The only technical part in this challenge is to manage to move the ISS into Moon's orbit then to succeed the Moon landing with thrusters and parachutes without destroying it. In case of landing failure and ISS deterioration, this could becomes a material stock for further Moon operations (~ 450 Tons of materials, equipment, wires, mechanical part, robotical parts, special experiment chambers, glasses and filled up materials, resources and tools for the operation).
Article : « Plutôt que de détruire la Station spatiale internationale, nous proposons de préserver sa valeur en la plaçant sur une orbite plus élevée »
Article : « La NASA veut faire s'écraser l'ISS sur Terre, mais des voix s'y opposent »