Uniqueness of the prime graph of $\mathrm{L}_{16}(2)$

We complete the proof that the simple group $\mathrm{L}_{16}(2)$ is uniquely determined by its prime graph among all finite groups thus giving the first example of a recognizable-by-graph group whose prime graph is connected. We bridge the gap in the argument from [1] which purported to establish the same result.