Am I interpreting it correctly that, yes, an Artificer in this situation would be able to reconstruct the petrified statue of his party member?
The Petrified condition states:
A petrified creature is transformed, along with any nonmagical object it is wearing or carrying, into a solid inanimate substance (usually stone). Its weight increases by a factor of ten, and it ceases aging.
The creature is incapacitated (see the condition), can't move or speak, and is unaware of its surroundings.
The spell fabricate states:
You convert raw materials into products of the same material. For example, you can fabricate a wooden bridge from a clump of trees, a rope from a patch of hemp, and clothes from flax or wool.
Choose raw materials that you can see within range. You can fabricate a Large or smaller object (contained within a 10-foot cube, or eight connected 5-foot cubes), given a sufficient quantity of raw material. If you are working with metal, stone, or another mineral substance, however, the fabricated object can be no larger than Medium (contained within a single 5-foot cube). The quality of objects made by the spell is commensurate with the quality of the raw material.
Creatures or magic items can't be created or transmuted by this spell. You also can't use it to create items that ordinarily require a high degree of craftsmanship, such as jewelry, weapons, glass, or armor, unless you have proficiency with the type of artisan's tools used to craft such objects.
In this example the "raw materials" used for fabricate would be the clump of rocks or stones or pebbles or dust that used to make up the stone shape of the petrified party member. The Artificer having proficiency in Mason's Tools allows them to create an item which "require a high degree of craftsmanship". The party member is of Medium size. Having traveled with this party member for a considerable amount of time the Artificer would have great knowledge of the petrified person.
The Artificer would not be creating a "Creature", which is explicitly forbidden per the description of fabricate. Per the Petrified condition, the creature is transformed into a "solid inanimate substance". The Artificer would be creating a solid inanimate statue of the person.
At that point, after 10 minutes and once the statue is complete, the petrified person could be restored using greater restoration spell.