It was written, but never published.

This 2013 thesis by Tyson Gern references it:

• D. Garfinkle. On the classification of primitive ideals for complex classical Lie algebras, IV. unpublished.

Fortunately, the same thesis discusses the proof of the type $D$ case (page 41), and gives some extra references, including another article by Garfinkle, which are likely to be relevant.

You also might want to consider contacting the author of the thesis.

It was written, but never published.

Tyson Gern's 2013 thesis references it:

• D. Garfinkle. On the classification of primitive ideals for complex classical Lie algebras, IV. unpublished.

Fortunately, the same thesis discusses the proof of the type $D$ case (page 41), and gives some extra references, including another article by Garfinkle, which are likely to be relevant.

You also might want to consider contacting the author of the thesis.

I was written, but never published.

This 2013 thesis by Tyson Gern references it:

• D. Garfinkle. On the classification of primitive ideals for complex classical Lie algebras, IV. unpublished.

Fortunately, the same thesis discusses the proof of the type $D$ case (page 41), and gives some extra references, including another article by Garfinkle, which are likely to be relevant.

You also might want to consider contacting the author of the thesis.

It was written, but never published.

This 2013 thesis by Tyson Gern references it:

• D. Garfinkle. On the classification of primitive ideals for complex classical Lie algebras, IV. unpublished.

Fortunately, the same thesis discusses the proof of the type $D$ case (page 41), and gives some extra references, including another article by Garfinkle, which are likely to be relevant.

You also might want to consider contacting the author of the thesis.