Using deep images from the Hyper Suprime-Cam (HSC) survey and taking advantage of its unprecedented weak lensing capabilities, we reveal a remarkably tight connection between the stellar mass distribution of massive central galaxies and their host dark matter halo mass. Massive galaxies with more extended stellar mass distributions tend to live in more massive dark matter haloes. We explain this connection with a phenomenological model that assumes, (1) a tight relation between the halo mass and the total stellar content in the halo, (2) that the fraction of in-situ and ex-situ mass at $r<10$ kpc depends on halo mass. This model provides an excellent description of the stellar mass functions (SMF) of total stellar mass ($M_{star}^{rm Max}$) and stellar mass within inner 10 kpc ($M_{star}^{10}$) and also reproduces the HSC weak lensing signals of massive galaxies with different stellar mass distributions. The best-fit model shows that halo mass varies significantly at fixed total stellar mass (as much as 0.4 dex) with a clear dependence on $M_{star}^{10}$. Our two-parameter $M_{star}^{rm Max}$-$M_{star}^{10}$ description provides a more accurate picture of the galaxy-halo connection at the high-mass end than the simple stellar-halo mass relation (SHMR) and opens a new window to connect the assembly history of halos with those of central galaxies. The model also predicts that the ex-situ component dominates the mass profiles of galaxies at $r< 10$ kpc for $log M_{star} ge 11.7$). The code used for this paper is available online: https://github.com/dr-guangtou/asap
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