By international law they can use weapons supplied by other nations even for long range strikes into Russia yes, to my knowledge it’s just a gentleman’s agreement that they follow the terms of the nation supplying them. Not really a point of contention though as it would be idiotic to violate those terms at risk of not being supplied anymore.

The only point of contention is whether supplying nations should decide to allow strikes into Russia with their equipment because Russia continues to threaten that it would see that as an act of war from the supplying nation. So legally nothing wrong with it but you have to weigh that decision with possibility of starting World War III or a nuclear apocalypse.