As both word embedding and context vectors capture these co-occurrence statistics (Levy and Goldberg, 2014), we can expect that context vectors share the same internal structure as embeddings.
moreover, for a fine-trained network, given any word w and its context h, the output layer's weight vector corresponding to w should specify a large inner-product score for the context h; thus these context vectors should approximate the weight vector of w. word embeddings and the output weight vectors should share the same internal structures and it is plausible to use a same set of sparse representations for both words and target-word weight vectors.