Based on these images and reading a bit on the internet, Neanderthals seem to not have a descended larynx.

The human larynx descended as early as 4 million years ago, as Australopithecus adapted to forage from the sea floor, and is a trait not found in Paranthropus who never went through a semi-aquatic phase as they diverged from Australopithecus as early as 6 million years ago (Popadin et al, 2017), and are found living alongside Australopithecines as early as 3.5 million years ago (Yohannes Haile-Selassie, nature.com, 2015).

The absence of a descended larynx therefore points to that the Neanderthal ancestry is not from the Australopithecus lineage, that led to Homo, but rather from Paranthropus. The alternative is a regression of the descended larynx, less parsimonious (higher cost evolutionarily. )

I wholeheartedly agree with Howells (1975) that the facial morphology of Homo specimens preceding the classic Neanderthal is more similar in these respects to the morphology of those following it than either is to the Neanderthal itself” (Rak, 1986, p. 163).

Theorem and reasoning

If the Neanderthal does not have a descended larynx (hypothesis here), then it is descended from Paranthropus

In case that is wrong, and it has a descended larynx, then it is descended from Australopithecus

References

1. Mitochondrial pseudogenes suggest repeated inter-species hybridization among direct human ancestors

2. New species from Ethiopia further expands Middle Pliocene hominin diversity